SOLUTION: Five cards are drawn from a standard deck of cards. Three are black and Two are red. a. How many possibilities are there? b. If exactly one of the red cards is a face card. H

Algebra ->  Probability-and-statistics -> SOLUTION: Five cards are drawn from a standard deck of cards. Three are black and Two are red. a. How many possibilities are there? b. If exactly one of the red cards is a face card. H      Log On


   

Question 1202684: Five cards are drawn from a standard deck of cards. Three are black and Two are red.
a. How many possibilities are there?
b. If exactly one of the red cards is a face card. How many possibilities are there?
Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


This is a straightforward problem for giving you practice using "n choose r"....

a. 3 black and 2 red

We need to choose 3 of the 26 black and 2 of the 26 red:

C(26,3)*C(26,2)

b. same but exactly one of the reds is a face card.

We need to choose 3 of the 26 black cards, 1 of the 6 red face cards, and 1 of the other 20 red cards:

C(26,3)*C(6,1)*C(20,1)

You can do the calculations.