So if I have five six sided dice what is the probability of getting three of a kind? Ie. 44452 or 63353.
I worked it out as
${{6 \choose 1}}$ ways of choosing the for the triple
${{5 \choose 3}}$ ways of choosing the dice for the triple
${{5 \choose 2}}$ ways of choosing the values for the single numbers
${{2 \choose 2}}$ ways of choosing the dice single numbers. (Only 1 one way of choosing 2 dice from remaining 2 dice).
$6^5$ total results from five six sided dice
So $\frac{{{6 \choose 1}}{{5 \choose 3}}{{5 \choose 2}}{{2 \choose 2}}}{6^5}$
And I get $\frac{25}{324}$...but it seems the actual answer is $\frac{25}{162}$ so where am I going wrong?