Question

Find the chance of throwing $12$ in a single throw with $3$ dice.

Answer 1

Dice 1	Dice 2	Dice 3	Number of Ways
6	5	1	$3!=6$
6	4	2	$3!=6$
6	3	3	$\frac{3!}{2!}=3$
5	5	2	$\frac{3!}{2!}=3$
5	4	3	$3!=6$
4	4	4	$\frac{3!}{3!}=1$

Number of ways of getting $12$ in a single throw of $3$ dice $=6+6+3+3+6+1=25$

Total number of ways $=$ $6^3$

Therefore, probability of getting $12$ in a single throw of $3$ dice $=\frac{25}{6^3}$