The probability of throwing three dice and getting three different numbers is:
$\frac{6(5)(4)}{6^3}$
but why can't I also do: P(three different numbers) = 1 - P(3 same numbers):
P(three different numbers) = 1 - $\frac {\binom{6}{1} \binom{1}{1} \binom{1}{1}}{6^3}$
Thanks