One of each court card

Topic: Random experiments and probability · more questions on this topic
‹ Three people, one birthday Three brothers in a random split ›

Four cards are drawn at once from a deck of 52, so the hand is an unordered set. Find the probability that the hand consists of one king, one queen, one jack and one ace.

Worked answer (click to show)

The sample space has \binom{52}{4} equally likely hands. The favourable hands choose one card from each of the four ranks, so there are 4^4 of them. The probability is 4^4/\binom{52}{4}.