A standard 52-card deck has 4 suits [. A 5-card hand can be chosen in any of of

Question

A standard 52-card deck has 4 suits [. A 5-card hand can be chosen in any of of 13 cards each . 52 ways - Bridge is a game where each of 4 players is dealt 13 cards, which means the whole deck is dealt. A hand has a distribution of suits, which is how many of each suit make up the 13 total. For example, [2 2 3 6] is the suit distribution of the hand: (2 hearts, 2 diamonds, 3 clubs and 6 spades). How many different hands with a 14 4 3 2] suit distribution can be dealt? How many different suit distributions are there? (4 4 3 21 is not different than [2 3 4 41, because order of the suits does not matter)

Explanation / Answer

Number of hands with a 4 4 3 2 suit disribution = 4!/2! * 13C4 * 13C4 * 13C3* 13C2 / 52C13 hands where the first 4! corresponds to the ways of choosin the suites and 2! since 4=4 is a common number

Different suits distributions= No. of non negaive solutions of x+y+z+a = 13 or 16C3

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