SOLUTION: Find the number of ways to get the following card combinations from a ​52-card deck. All diamonds in a​ five-card hand

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Question 1203034: Find the number of ways to get the following card combinations from a ​52-card deck.
All diamonds in a​ five-card hand
Answer by ikleyn(52776) About Me  (Show Source):
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Find the number of ways to get the following card combinations from a ​52-card deck.
All diamonds in a​ five-card hand
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There are 52 cards in a standard card deck; 1/4 of them, i.e. 52/4 = 13 are diamonds.


Therefore, the number of all different quintuples consisting of all diamonds is

    C%5B13%5D%5E5 = 1287.    ANSWER

Solved.

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In this problem, the order of cards does not matter,
so we use COMBINATIONS as an appropriate mathematical object/conception.

On  Combinations,  see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.