Question

At an election, 3 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

First, 10 men have to be chosen out of 45 men=45C10 ways.
Second,out of the remaining (45-10=35), 15 men have to chosen=35C15 ways.
Finally, out of the remaining (35-15-20), 20 men have to chosen in 20C20 ways.

So total number of ways are= 45C10*35C15*20C20
=45!/(10!*15!*20!)