Question

In how many ways can $10$ identical blankets be given to $3$ beggars such that each receives at least one blanket?

Answer 1

We have $10$ blankets and $3$ beggers

It is must that we have to give $1$ blankets for $1$ beggar.

As $1$ blankets for $1$ beggar $=3$ blankets compulsory

$10-3=7$ blankets left

$7$ blankets distributed among $3$ beggars

The no. of ways in which ${}^{\prime }{n}^{\prime }$ objects distributed for ${}^{\prime }{r}^{\prime }$ groups is ${}^{n+r-1}{C}_{r-1}$. Here $n=7$

$r=3$

${}^{7+3-1}{C}_{3-1}{=}^{10-1}{C}_2$

${=}^9{C}_2$