Choose 5 cards from a full deck of 52 cards with 13values (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A) and 4 kinds(spade, diamond, heart, and club). Count how many possible ways to geta(a)Two-pairs: Two pairs plus another card of a different value, for example:(b)Flush: five cards of the same suitbutdifferent values, for example: (c)Full house: A three of a kind and a pair, for example: (d)Four of a kind: Four cards of the same value, for example:

Answers

Answer 1

Answer:

a) 182 possible ways.

b) 5148 possible ways.

c) 1378 possible ways.

d) 2899 possible ways.

Step-by-step explanation:

The order in which the cards are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question, we have that:

There are 52 total cards, of which:

13 are spades.

13 are diamonds.

13 are hearts.

13 are clubs.

(a)Two-pairs: Two pairs plus another card of a different value, for example:

2 pairs of 2 from sets os 13.

1 other card, from a set of 26(whichever two cards were not chosen above). So

[tex]T = 2C_{13,2} + C_{26,1} = 2*\frac{13!}{2!11!} + \frac{26!}{1!25!} = 182[/tex]

So 182 possible ways.

(b)Flush: five cards of the same suit but different values, for example:

4 combinations of 5 from a set of 13(can be all spades, all diamonds, and hearts or all clubs). So

[tex]T = 4*C_{13,5} = 4*\frac{13!}{5!8!} = 5148[/tex]

So 5148 possible ways.

(c)Full house: A three of a kind and a pair, for example:

4 combinations of 3 from a set of 13(three of a kind ,c an be all possible kinds).

3 combinations of 2 from a set of 13(the pair, cant be the kind chosen for the trio, so 3 combinations). So

[tex]T = 4*C_{13,3} + 3*C_{13.2} = 4*\frac{13!}{3!10!} + 3*\frac{13!}{2!11!} = 1378[/tex]

So 1378 possible ways.

(d)Four of a kind: Four cards of the same value, for example:

4 combinations of 4 from a set of 13(four of a kind, can be all spades, all diamonds, and hearts or all clubs).

1 from the remaining 39(do not involve the kind chosen above). So

[tex]T = 4*C_{13,4} + C_{39,1} = 4*\frac{13!}{4!9!} + \frac{39!}{1!38!} = 2899[/tex]

So 2899 possible ways.


Related Questions

Suppose that a loan of $8000 is given at an interest rate of 13% compounded each year.
Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.
si
(b) Find the amount owed at the end of 2 years.

Answers

Answer:

9040

10215.20

Step-by-step explanation:

compound interest that compounds yearly works as follows

PV(1+i)^n

just plug in the numbers

8000(1.13)^1= 9040

8000(1.13)^2=10215.20

Which expression is equivalent to 3x + 3 x + 3x

3x3

9x

9x3

27x

Answers

The answer to your question is 9x

please help on this one.

Answers

Answer:

it's A

Step-by-step explanation:

look at the bolded line, it's after 4.4 which would mean z> 4.4

Answer:

A

Step-by-step explanation:

so we have a less than sign, which immediately tells us this going to be going left as 4.4 is greater. and obviously since the number is 4.4, the graph will have targeted that number. Hope this helps!

A round pizza was cut into 8 equal pieces. 7 pieces were eaten. What is the angle measure of the piece not eaten?

Answers

Answer:

sorry didnt mean to answer

edit: it should be around 45

3(2k-5)=6(k-4)+9
Determine whether the equation has one solution, no solution, or infinitely many solutions

Answers

Answer:

many solutions

Step-by-step explanation:

3×2k=????

3×5=??

6×k=??

6×4=??

then put all those together in a 2 step equation and then add 9 to the answer

The equation 3(2k-5)=6(k-4)+9 has infinitely many solutions.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

3(2k-5)=6(k-4)+9

In the given equation k is the variable

Now apply distributive property to the RHS and LHS wherever it is required

6k-15=6k-24+9

6k-15=6k-15

Shift all terms to one side

6k-15-6k+15=0

0=0

Hence the equation 3(2k-5)=6(k-4)+9 has infinitely many solutions.

To learn more on Equation:

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between x=2 and x=3, which function has a greater average rate of change than f(x)=2^x has?

Answers

Answer: f(3)

Step-by-step explanation:

First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.

[tex]y=2^x\\\ln(y)=x \ln(2)[/tex]

Implicitly differentiate the left side and take the derivative of the right side

[tex]\frac{y'}{y} =\ln(2)[/tex]

Multiply both sides by 'y' which was defined as 2^x

[tex]y'=\ln(2)*2^x[/tex]

Plug in x = 2 and x = 3 to see which slope is larger

[tex]y'=\ln(2)*2^2=4\ln(2)\\y'=\ln(2)*2^3=8\ln(2)[/tex]

The average cost for vacation is $1050 if a family borrows money for the vacation at an interest rate of 11.9% for six months what is the total cost of the vacation including the interest on the loan

Answers

The answer to this question is 1764

Pls help I have today to finish this

Answers

Answer:

50

Step-by-step explanation:

because 50 pints

Answer:

50

Step-by-step explanation:

How to write log6(35) in exponential form?

Answers

6^?=35 so 6 to the power of something will equal 35. Another example would be if you had log6(36)=2 would be 6^2=36 to find the power for your answer I would recommend a calculator hope this helps!

Answer:

10^35=6

Step-by-step explanation:

All you need to remember is the picture above and you could do it.

8k - 6 = 10k + 6
No idea how to figure this out

Answers

8k - 6 = 10k + 6

K= -6

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    8*k-6-(10*k+6)=0

Step by step solution :

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  -2k - 12  =   -2 • (k + 6)

Equation at the end of step

1

:

STEP

2

:

Equations which are never true:

2.1      Solve :    -2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2      Solve  :    k+6 = 0

Subtract  6  from both sides of the equation :

   Which gives k = -6

Answer: K = -6

Step-by-step explanation:

When you add or subtract on one side, you have to do the same to the other side. You also have to get all the numbers with vairables on one side, and the ones without on the other side.

When you have a positive number, if you want to bring it to the other side, you have to subtract it. For example, if you want to bring 8k from the left side onto the right side, you have to subtract 8k from a number on the right side.

For this equation, lets bring all the numbers with vairables onto one side, and the ones without vairables on the other side. The ones with vairables will be on the left, and the numbers without will be on the right.

To bring 10k from the right side to the left, we have to subtract 10k from 8k. 8k - 10k = -2k.

Now we have to bring the -6 from the left side onto the right side. Since -6 is a negative number, we have to make it into a positive number to swap it to the other side. So it because 6. We add 6 to -6, and 6 to 6. The leaves the left side to be -2k, and the right side to be 12.

Now we have to divide. 12 ÷ -2 = -6. Therefore, k = -6. I hope this helps, and good luck on whatever you're doing :D

can yoy please help solve yhis problem.2/5b+1=11​

Answers

Answer:

(2/5)*b+1 = -11 // + 11

(2/5)*b+1+11 = 0

2/5*b+12 = 0 // - 12

2/5*b = -12 // : 2/5

b = -12/2/5

b = -30

b = -30

Step-by-step explanation:

hope this helped :)

Step-by-step explanation: First: Multiply 2/5 by 2. 5x2=10. 10 then turns into o a whole number +1=11.

10+1=11

I need help with this please

Answers

the correct answer is A) 10x + 30

Answer:

The answer is "10x+30"

Step-by-step explanation:

Your cousin borrows $1125 to repair her car. The simple annual interest rate is 10%. She makes equal monthly payments of $25. How many years will it take to pay off the loan?PLEASE EXPLAIN. I know interest =. principal times rate times time

Answers

Answer:

neat

Step-by-step explanation:

Which of the following statements is true? A square is ALWAYS a rectangle. A rectangle is ALWAYS a square. A rectangle is NEVER a square. A square is NEVER a rectangle.

Answers

A square is always a rectangle

Answer:

A square is always a rectangle

Step-by-step explanation:

50 points! I only want mhanifa to help me so no one else answer unless you actually know how to do it

Answers

Answer:

Bbc

Step-by-step explanation:

What is the value of (1)³ ?

Answers

Step-by-step explanation:

the value of 1³ is 1* 1*1 = 1

Hope it will help :)

Value of 1^3 is 1 times its self 3 times so it would be 1•1•1=1 because some times anything is itself

Barbara has a part-time lawn-mowing job. The table below shows the amount of money Barbara earned for different numbers of hours of work:


Barbara's Earnings from Lawn Mowing
Number of Hours Worked Money Earned (dollars)
5 40
6 48
8
56


Part A: What are the missing numbers in the table? Show your work.

Part B: Barbara also works part time at a theme park. The ratio of the number of hours Barbara works at the park to the money she earns in dollars is 1:9. Create a table to show the money earned by Barbara for 5, 6, and 8 hours of work at the theme park.

Part C: How many more dollars does Barbara earn working at the theme park for 5 hours than mowing lawns for 5 hours? Show your work.

Answers

Answer:

Part A: 5-40

6-48

8-64

7-56

Part b:

1-9

5-45

6-54

8-72

Part c:

Theme park

5-45

Mowing lawns

5-40

$5

Step-by-step explanation:

Part A: 5x8=40

6x8=48

8x8=64

56/7=8

Part C: Every 5 hours working at the theme park she earns 45 dollars, when mowing lawns she earns 40 dollars 45-40 equal $5 extra dollars at the theme park.

Pls help me I’ll make brainliest

Answers

Answer:

60 cents for 1 pound

Step-by-step explanation:

2 pounds = $1.20

1 pound =  60 cents

When paying for a restaurant order, a customer's total for food was $30.00. What is a 18% tip for that total?

Answers

Answer:When paying for a restaurant order, a customer's total for food was $30.00. What is a 18% tip for that total? I WILL GIVE BRAINLEIST PLEASE

Step-by-step explanation:

The answer is 5.40 and also like they said you can round if you need too

what function equation is represented by the graph

f(x) = 4^x+5

f(x) = 3^x+4

f(x) = 3^x+5

f(x) = 4^x+4

Answers

Answer: C

The graph goes up along the Y-axis at 5 (+5)

Answer:

B

Step-by-step explanation:

We know that when x=0 y=5

B and D are the only ones that meet this criteria

we know that when x=2 y= 13 or so

D no longer works

it has to be B

In a student council election, Kyle receives 54 votes for president. If Kyle receives 60% of the votes, how many students vote in the election?

Answers

Answer:

90

Step-by-step explanation:

60%-> 54

100%-> 90

There are 90 students vote in the election.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100

Given that

In a student council election, Kyle receives 54 votes for president.

Now,

Let total student votes in election = x

Hence we can formulate

60% of x = 54  

60/100 × x = 54

60x = 5400

x = 90

Therefore,  There are 90 student votes in the election.

Learn more about the percent visit:

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David keeps records of his monthly earnings. Last month he worked 140 hours and earned $3700. This month he worked 120 hours and earned $3200. Part A: what is David's rate of pay?

Answers

Id say about 26$ per hour bc 3700 divided by 140 is 26.4 and 3200 divided by 120 26.6

Suppose you buy 2 marbles for $0.16 each. You pay for it with 4 quarters. How much change should you get back? Enter your answer.

Answers

Answer: You should get 0.68 back

Step-by-step explanation: I just did a test and got 100%

Answer:

3 $0.16 = $0.48

or

4 $0.25 = $1.00 hope this helps

Step-by-step explanation:

Brandi is the star of her school's volleyball team. In the first game of the season she had 9 "kills". Then she had the
same number of kills in each of the next 4 games. She had 49 kills in the five games. How many did she get per game
in the the last 4 games?
write and solve an equation

Answers

Answer: 36

Step-by-step explanation:

I'm not sure if this is 100% right this question was kinda messing with my brain , but if it's like asking how much she had in the 4 games all you had to do was add 9+9+9+9 or to make it easier you can just multiply 9 times 4 but I hope this is right.  

6/q= k/27

what is q?
what is k?​

Answers

6=q
27=k
That’s the answer right ??

Help ASAP!!!! Will mark you brainliest

Answers

Answer:

OK so... I know the answer to x(4)+4x(3)+5x(2)-4x-4 =     -4

The part i don't understand is the f(x)=k=1 part.

Step-by-step explanation:

So overall the only answer I know is -4 Sry i couldn't help more.

Brainliest?

Which one goes in the box ? Pls help I’ll mark you brainly

Answers

Answer:

5 is co efficient

8x is term

9 is constant

Step-by-step explanation:

Please help ASAP really need this

Answers

Answer:

[tex]21.79 + c \leq 25[/tex]

Joshua can spend up to 3.21 on a card.

Step-by-step explanation:

[tex]21.79 + c \leq 25[/tex] is the correct equation because Joshua is spending 21.79 on flowers, a certain amount on the card, and the maximum he can spend is 25. That is why you use the less than or equal to sign.

To solve, first subtract 21.79 from both sides to get: [tex]c \leq 3.21[/tex]. This means that Joshua can spend up to 3.21 on a card.

Hope it helps!

PLEASE ANSWER FAST I HAVE 30MINS!!!!!! Which graph shows the result of dilating this figure by a factor of 4 about the origin? On a coordinate plane, rectangle A B C D has points (negative 1, 1), (3, 1), (3, negative 1), (negative 1, negative 1). On a coordinate plane, rectangle A prime B prime C prime D prime has points (negative 4, 4), (12, 4), (12, negative 4), (negative 4, negative 4). On a coordinate plane, rectangle A prime B prime C prime D prime has points (negative 2, 2), (6, 2), (6, negative 2), (negative 2, negative 2). On a coordinate plane, rectangle A prime B prime C prime D prime has points (negative 0.25, 0.25), (0.75, 0.25), (0.75, negative 0.25). (negative 0.25, negative 0.25). On a coordinate plane, rectangle A prime B prime C prime D prime has points (negative 0.5, 0.5), (1.5, 0.5), (1.5, negative 0.5), (negative 0.5, negative 0.5).

Answers

Answer:

2

Step-by-step explanation:

abshxhdbxbjsbxbsbxnd

Every hour, a research assistant removes half the mass of a bacteria culture originally weighing 4,800 micrograms to observe under a microscope. The research assistant will stop this process once the mass is equal to 300 micrograms.

Which equation represents this situation, and after how many hours will the research assistant stop removing half the mass of the bacteria culture?

Answers

Answer:

Step-by-step explanation:

4,800 mcg × 0.5^t = 300 mcg

0.5^t = 1/16 = (1/2)⁴

t = 4

Answer:

[tex]4,800\left(\frac{1}{2}\right)^{t} \, = \, 300; \ 3 \ \text{hours}[/tex]

Step-by-step explanation:

Every hour, the research assistant is removing half the mass from the original 4,800 micrograms of the bacteria culture. So, the mass remaining after t hours can be represented by an exponential expression, a(b)t, where a is the initial mass of the bacteria culture and b is the base of the exponent that represents the decay factor. Since half of the mass of bacteria is being removed every hour, half of the mass remains. So, b = [tex]\frac{1}{2}[/tex]. The exponential expression for this situation is [tex]4,800\left(\frac{1}{2}\right)^{t}[/tex].

The research assistant will stop removing half the mass from the original bacteria culture after the original bacteria culture has a mass of 300 micrograms. Hence, set the expression for the mass remaining after t hours equal to 300.

[tex]4,800\left(\frac{1}{2}\right)^{t} \, = \, 300[/tex]

In order to solve this equation for t, the base needs to be isolated. Divide both sides of the inequality by 4,800.

[tex]\begin{array}{rclC40C40} 4,800\left(\frac{1}{2}\right)^{t} &=& 300\\ \left(\frac{1}{2}\right)^{t} &=& \frac{1}{16} \end{array}[/tex]

Next, rewrite the base of [tex]\frac{1}{16}[/tex] as a power of [tex]\frac{1}{2}[/tex]. Then, set the exponents equal to each other to solve for t.

[tex]\begin{array}{rclC40C40C30} \left(\frac{1}{2}\right)^{t} &=& \frac{1}{16} \\ \left(\frac{1}{2}\right)^{t} &=& \left(\frac{1}{2}\right)^{4} \\ t &=& 4 \end{array}[/tex]

So, after 4 hours the research assistant will stop removing half the mass of the bacteria culture.

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