Question

In how many ways can $12$ things be divided equally among $4$ persons?

Answer 1

As there are $12$ things that needs to be divided amongst $4$ people, so each person would get $3$ things.

Number of ways of selecting $3$ things out of $12$ things for $1^{st}$ person =${}^{12}{C}_3=220\text{ways.}$

Number of ways of selecting $3$ things out of $9$ things for $2^{nd}$ person =${}^9{C}_3=84\text{ways.}$

Number of ways of selecting $3$ things out of $6$ things for $3^{rd}$ person =${}^6{C}_3=20\text{ways.}$

Number of ways of selecting $3$ things out of $3$ things for $4^{th}$ person =${}^3{C}_3=1\text{way.}$

Hence, total number of ways $=220\times 84\times 20=369600\text{ways.}$