[Math] Bridge hand Combination/Permutation

combinatoricspermutationsprobability

A Bridge hand consists of 13 cards from a deck of 52 cards. In how many ways can a (bridge) hand
consisting of 5 spades(♠), 4 hearts(♥), 4 diamonds(♦) and 0 clubs(♣) be selected?

Best Answer

There are $13 \choose 5$ ways of choosing $5$ spades.

There are $13 \choose 4$ ways of choosing $4$ hearts.

There are $13 \choose 4$ ways of choosing $4$ diamonds.

So there are $13 \choose 5$$\times$$13 \choose 4$$\times$$13 \choose 4$ ways of selecting a bridge hand with $5$ spades, $4$ hearts, $4$ diamonds, and $0$ clubs.

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