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

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) (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.
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