SOLUTION: A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total

Algebra ->  Permutations -> SOLUTION: A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total       Log On


   

Question 1208649: A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all.
How many 7-card hands will consist of exactly 2 kings and 3 queens?

Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

We choose 2 kings from 4 kings in  C%5B4%5D%5E2 = %284%2A3%29%2F2 = 6 different ways.

We choose 3 queens from 4 queens in  C%5B4%5D%5E3 = 4 different ways.

We choose (7-2-3) = 2 another cards from the pool of 52-4-4 = 44 another cards 
in  C%5B44%5D%5E2 = %2844%2A43%29%2F2 = 22*43 = 946 different ways.


Thus the total number of different choices is  6*4*946 = 22704.    ANSWER

Solved.



Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

We choose 2 kings from 4 kings in  C%5B4%5D%5E2 = %284%2A3%29%2F2 = 6 different ways.

We choose 3 queens from 4 queens in  C%5B4%5D%5E3 = 4 different ways.

We choose (7-2-3) = 2 highlight%28cross%28another%29%29 other cards from the pool of 52-4-4 = 44 highlight%28cross%28another%29%29 other cards 
in  C%5B44%5D%5E2 = %2844%2A43%29%2F2 = 22*43 = 946 different ways.


Thus the total number of different choices is  6*4*946 = 22704.    ANSWER

Solved.