Question

Consider three boxes, each containing $10$ balls labelled $1,2,...,10$ Suppose one ball is randomly drawn from each of the boxes. Denote by $n_i$ , the label of the ball drawn from the $i^{th}$ box, $(i=1,2,3)$ Then, the number of ways in which the balls can be chosen such that $n_1<n_2<n_3$ is

Answer 1

Answer: 120

Collecting different labels of balls drawn $=10\times 9\times 8$
$Q$ arrangement is not required
$\therefore$ the number of ways in which the balls can be chosen is,
$\frac{10\times 9\times 8}{3!}=120$