Question 1152098: Five cards are drawn from a pack of shuffled cards without replacement. Find the probability that
a. 4 are aces and 1 is a king
b. 3 are 10's and 2 are jacks
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
In each case, you are choosing 5 of the 52 cards; the number of possible combinations is 52 choose 5 = 2598960. That will be the denominator of the probability fraction.
a. you need to choose all 4 of the 4 aces, 1 of the 4 kings, and 0 of the other 44 cards: (4 choose 4)*(4 choose 1)*(44 choose 0) = 1*4*1 = 4. Then
P(4 aces and 1 king) = 4/2598960 = 1/649740
b. you need to choose 3 of the 4 tens, 2 of the 4 jacks, and 0 of the other 44 cards: (4 choose 3)*(4 choose 2)*(44 choose 0) = 4*6*1 = 24. Then
P(3 aces and 2 jacks) = 24/2598960 = 1/108290
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