# Probability of different numbers on 3 dice

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

• The complementary event of "three different" is "three not all different." The complementary event of "three the same" is "three not all the same." Sep 25 at 16:25