Question

In how many ways can $5$ identical balls be arranged in $3$ boxes, such that no box is empty?

Answer 1

Total number of ways of dividing $5$ identical bolls in $3$ distinct boxes so that none of boxes is empty

${=}^{5-1}{c}_{3-1}$ (Using the formula ${}^{n-1}{c}_{r-1}$)

${=}^4{c}_3$

$=\frac{4!}{(4-2)!2!}$

$=\frac{4\times 3\times 2!}{2!2!}$

$=6.$