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Combinatorics

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Three-of-a-kind from Five Dice

COMBIN-N8EWLH

Roll five standard 6-sided dice simultaneously.

What is the probability that we get three-of-a-kind (for instance three 5's, one 6, and one 2)?

A

$\cfrac{{5\choose 3}}{6^5}$

B

$\cfrac{{6\choose 3}}{6^5}$

C

$\cfrac{5{5\choose 3}}{6^5}$

D

$\cfrac{25}{162}$

E

$\cfrac{25}{1296}$