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

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,
$\frac{10 \times 9 \times 8}{3!}=120$