Question

At an election three districts are to be canvassed by $10,15$ and $20$ men respectively. If $45$ men volunteer, in how many ways can they be allotted to the different districts?

Answer 1

Let us consider there are total of $45$ letters of which
$10⟶$ are of type ${}^{\prime }{1}^{\prime }$
$15⟶$ are type ${}^{\prime }{2}^{\prime }$
$20⟶$ are type ${}^{\prime }{3}^{\prime }$
Now, total number of arrangement of letters $=\frac{45!}{10!15!20!}$
Similarly, $45$ men can be arranged in $3$ districts in
$=\frac{45!}{10!15!20!}$ no. of ways