Combinatorics

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Four-of-a-kind from Five Dice

COMBIN-DR9XVL

Roll five standard 6-sided dice simultaneously.

What is the probability that we get four-of-a-kind (for instance four 6's and one 3)?

A

$\cfrac{{5\choose 4}}{6^5}$

B

$\cfrac{{6\choose 4}}{6^5}$

C

$\cfrac{5\cdot{6\choose 4}}{6^5}$

D

$\cfrac{5}{1296}$

E

$\cfrac{6\cdot{5\choose 4}\cdot5}{6^5}=\frac{25}{1296}$