What is the chance of being dealt 4 of a kind in a standard deck of 52 cards?

Question

Thirteen cards are distributed evenly among 4 sets from a standard deck of cards. What is the chance of one set containing a 4 of a kind? (assume deck is completely shuffled and randomized)

Answer 1

Four of a kind is four cards with the same rank and 1 other card for the five card hand. There is a possibility of 13 four card ranks in a deck so this can be expressed as C13,1 = 13!/12!1! = 13. Then choose a fifth card from the other 48 (after the first four.) This is C_48,1 = 48. 

 

probability of four of a kind = 624/C_52,5 = 0.00024