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Single-suit hands

CombinatoricsEasy

How many different hands of $5$ cards from a standard $52$ -card deck have all $5$ cards in the same suit? Straights count as well, and the order of cards in a hand does not matter.

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Hint

Choose the suit first, then the cards inside it.

Solution

There are $4$ ways to choose the suit.
Within that suit there are $13$ cards, and choosing $5$ of them gives $(5 13) = 1287$ hands.
The total is $4 \times 1287 = 5148$ .

Answer: $5148$

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