easy Probability

Three of a Kind

A release-checked easy problem for training Cards, Combinations and Permutations, Combinatorics.

Question

A $5-$card hand is called a three-of-a-kind if it consists of $3$ cards of one rank and $2$ cards of two other distinct ranks. To the nearest ten-thousandth, find the probability that a random $5$ card hand drawn from a standard deck of cards is a three-of-a-kind.

Practice focus

This Probability problem is tagged Cards, Combinations and Permutations, Combinatorics. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.