Mathematics - Permutation & Combination Question with Solution | TestHub

Given,

Rooms are identical,

So, total ways to distribute $5$ employees into $4$ rooms are:

$5,0,0,0\Rightarrow 1$ way

$4,1,0,0\Rightarrow \frac{5!}{4!}=5$ ways

$3,2,0,0\Rightarrow \frac{5!}{3!2!}=10$ ways

$2,2,0,1\Rightarrow \frac{5!}{2!2!2!}=15$ ways

$2,1,1,1\Rightarrow \frac{5!}{2!{\left(1!\right)}^{3}3!}=10$ ways

$3,1,1,0\Rightarrow \frac{5!}{3!2!}=10$ ways

Total $\Rightarrow 1+5+10+15+10+10=51$ ways