Question 1203034
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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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<pre>
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[13]^5}}} = 1287.    <U>ANSWER</U>
</pre>

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 &nbsp;Combinations, &nbsp;see introductory lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>

in this site.