A probability problem by A Former Brilliant Member
From a standard deck of playing cards, a hand of five cards is chosen. How many different five-card hands consist of two kings and three queens? (This hand is an example of a “full house” in the game of poker.)
The answer is 24.
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1 solution
There are 4 C 2 ways of choosing two kings from the four kings in the deck and 4 C 3 ways of choosing three queens from the four queens. By the counting principle, there are 4 C 2 × 4 C 3 ways of choosing two kings and three queens. There are 2 4 ways of choosing two kings and three queens.