Question

Three ladies have brought one child each for admission to a school. The principle wanted to interview the six persons one by one subject to the condition that no mother is interviewed before her child. Then find the number of ways in which interviews can be arranged

Answer 1

$6!=720$,ways the interview six people with no constraint.

Divide by 2 to account for ordering for each child/mother

(e.g. given an ordering of six people, there is exactly one "equivalent" ordering by switching mother w/s his child).

hence answer is = $\frac{6!}{2^3}$

$\Rightarrow \frac{720}{8}$

$\Rightarrow 90$