SOLUTION: You are dealt five cards from a standard and shuffled deck of playing cards. Note that a standard deck has 52 cards and four of those are kings. What is the probability

Algebra ->  Probability-and-statistics -> SOLUTION: You are dealt five cards from a standard and shuffled deck of playing cards. Note that a standard deck has 52 cards and four of those are kings. What is the probability       Log On


   

Question 1069835: You are dealt five cards from a standard
and shuffled deck of playing cards. Note
that a standard deck has 52 cards and four
of those are kings. What is the probability
that you'll have exactly three kings in your
hand?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
There are 4 ways 3 kings can be chosen 4C3
Of the 48 cards left, there are 48C2 ways 2 cards can be chosen
This is over 52C5
4*1152/2598960=0.00177
A second way to look at it is that there are 10 ways the king can appear in 5 cards when there will be 3 kings.
The first way is (4/52)(3/51)(2/50)(48/49)(47/48)
The second way is (48/52)(47/51)(4/50)(3/49)(2/48), and the other 8 ways will have the same numerator and same denominator, just ordered differently. The result is multiplied by 10 and get the same result. Note: this is not the probability for 3 of a kind, but a more rare 3 of a kind, 1 rank.