Question

In how many ways can five things be divided between two persons?

Answer 1

There are different ways of dividing $5$ things between two persons

$P_1$ $P_2$ No. of ways
$0$ $5$ $={}^5{C}_5\times 2!=2$
$1$ $4$ $={}^5{C}_4\times 2!=10$
$2$ $3$ $={}^5{C}_3\times 2!=20$
$\therefore$ Total no. of ways $=32$
Removing null cases i.e., no one receives ${}^{\prime }{0}^{\prime }$
$\therefore$ Total no. of ways $=30$