SOLUTION: suppose you are dealt a hand of three cards at random from a deck of 32 cards consisting of 4 aces, 4 2s, 4 3s and so on up to 4 8s. what is the probability that your hand will hav

Algebra ->  Probability-and-statistics -> SOLUTION: suppose you are dealt a hand of three cards at random from a deck of 32 cards consisting of 4 aces, 4 2s, 4 3s and so on up to 4 8s. what is the probability that your hand will hav      Log On


   

Question 440625: suppose you are dealt a hand of three cards at random from a deck of 32 cards consisting of 4 aces, 4 2s, 4 3s and so on up to 4 8s. what is the probability that your hand will have atleast 2 4s? what is the probability that none of your cards will have the same numeric value?
i tried (4/32)(3/31) for the first one and it was wrong
i tried (1/32)(1/31)(1/30) for the second but that didn't work either
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the number of different 3 card hands from a deck of 32 cards is ___ 32C3

the number of different hands containing 2 fours is ___ (4C2)*28

the number of different hands containing 3 fours is ___ (4C3)

the probability of at least 2 fours ___ {[(4C2)*28] + 4C3} / 32C3


for a hand of no matching cards
___ possibilities for 1st card ___ 32
___ possibilities for 2nd card ___ 28
___ possibilities for 3rd card ___ 24
___ since order does NOT count, the product is divided by 3!

probability of no matching cards ___ [(32*28*24) / 3!] / 32C3