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What happened to sevens?

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###### Asked in Board Games, Statistics, Probability

### Five cards are dealt at random from a regular deck of 52 playing cards Find the probability that three are sevens?

First, determine the probability of three sevens and two
non-sevens, then worry about the permutations. The probability is
the number of sevens, sevens minus one, sevens minus two,
non-sevens, and non-sevens minus one; all over the number of cards
left in the deck with each draw. The permutations of this
configuration are 10 (you can verify this by arranging five cards
as desired).
P(exactly three sevens) =
10*(4/52)(3/51)(2/50)(48/49)(47/48)
= (47)/(13*17*25*49) = 47/270,725
Those are pretty small odds, haha.