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:

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.

Which triangle most likely has the angles 56°, 48°, and 76°?
A. triangle A
B. triangle B
C. triangle C
D. triangle D

6+(9-1)2 divided by 4x (1/2)

cos=0.985 rounded to nearest tenth

Can you help me on question six?!

its something about cookies

If x is a positive integer, which of the following must be an even integer that is twice the value of an odd integer.

A. 2x
B. 2x + 1
C. 2x + 2
D. 4x + 1
E. 4x + 2

Grayson is going to invest $710 and leave it in an account for 17 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest hundredth of
a percent, would be required in order for Grayson to end up
with $920?

Solve for x and y. Please help, I will mark as brainliest and give many points

Find the length of side x

Which fraction is equivalent to (7-3)*3/10^4-10^2
A. 16/25
B. 1/25
C. 8/1125
D. 16/2475

A random number generator is set to produce integers from 1 to 10.
About how often would you expect to get an even number in 300 trials?
You would expect to get an even number about
times.

do this for brainliest! :)

(This is fundamental Counting principle) choosing from 35 different flavors of ice cream; one, two or three scoops; and sugar or waffle cone.

what is -6(a + 8) simplified?

s is inversely proportional to t.
When s
0.4, t = 4
Work out s when t = 0.8​

At Cascadia College, students need to take a 100 level Math and English courses plus an optional Philosophy course. In any quarter, the college needs to make available 4 less English sections than Math sections. In any quarter student demand for the optional Philosophy course is half as many sections as English sections. Available classrooms limit the total sections of all three courses to 44
Given these constraints how many sections of each course should the college make available each quarter to meet demand?
Math sections =
English sections =
Philosophy sections =

F(t)=212-6t
what is the value of t when F (t) = 140?

​

help please (will mark brainliest or however you spell it)

An ice company charges $8.16 for 6 bags of ice . If you buy 8 bags of ice how much would it cost you ?

The formula V equals S to the third power gives the volume V of a cube with the side length S the volume of a cube that has a side length of 3 inches is__?__ inches cubed

Find the value of x.
35
21
Х
X=
= [?]
Help

r+4 at r=13 help me ​

Divide 4 1/2 by the following unit fractions.

1/8

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

Sophie has 5 pieces of string that are each 5 feet long. Cooper has 4 pieces of string that are each
3 feet long. Estimate how much more string Sophie has than Cooper has. Enter your answer in the bo

If x = 4, what is the value of 10x + 147

20 points Which of the following is NOT an advantage of using wind turbines to generate wind power? Wind turbines are not suitable for all geographical locations. O Wind turbines are affordable. Wind turbines do not emit carbon dioxide and do not require sunshine. O Wind turbines cause little disruption of ecosystems.​

In the triangle below, the measure of angle A = 52°. Find the measure of angle C.

A coordinate plane.

Which statements are true? Check all that apply.
The line that goes through the points (3,7) and (–2,7) is a horizontal line.
The equation x = –8 is a vertical line that goes through the point (–8,3).
The line that goes through the points (0,5) and (0,–7) is a vertical line.
The points on a horizontal line have the same x-coordinate.

List the factors in the expression 4r + 5s +8.
PLZ HELP MEEEEE!!!!!