Three dice are rolled.

Question

Three dice are rolled. If the probability of getting different numbers on all three is $\dfrac{p}{q}$ (coprime), find $q-p$.

Accepted Answer

$$P = \frac{{}^6C_3\times3!}{6^3} = \frac{20\times6}{216}=\frac{120}{216}=\frac{5}{9}$$

$p=5,q=9 \implies q-p=4$.

Solutions · 1