Question

A fair die is thrown three times and the three outcomes are multiplied. Let $p$ be the probability that the outcome is divisible by $16$. Then the value of $\frac{7}{18p}$ is

Answer 1

Let the outcome on two throws of the die be $(4,4)$
Then number of possible combinations is $5\times \frac{3!}{2!}+1=16$

If outcome on two throws of the die is $(2,2)$ or $(6,6)$,
then number of possible combinations is $2\times \frac{3!}{2!}=6$

If outcome on three throws of the die is $(2,4,6)$,
then number of possible combinations is $3!=6$
$\therefore p=\frac{28}{216}=\frac{7}{54}$