A four-of-a-kind is a 5-card hand in which 4 of the cards are of the same denomination, such as J-J-J-J-6, 7-7-7-7-A, or 2-2-2-2-5

5-card-hand
same-denomination

#1

A four-of-a-kind is a 5-card hand inwhich 4 of the cards are of the same denomination,
such as J-J-J-J-6, 7-7-7-7-A, or 2-2-2-2-5.
b) What is the probability of getting four of a
kind?

Answer:

there are 13 denominations of cards … each four-of-a-kind has a 5th card, which is one of 12 … so there are (13 * 12) possible four-of-a-kind hands … there are 52C5 possible 5 card hands … the probability of four-of-a-kind is [(13 * 12) / 52C5]