Question

How many different committees of 5people can be chosen from 10 people

Answer 1

Solution:

Let's give each people one number: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;

We can write it like set: $A={1,2,3,4,5,6,7,8,9,10}$, this is set with 10 elements. Now, we need to find number of subsets of set A which equal number of different committees with 5 people:

$N=\frac{n!}{(n-m)!m!}$ - this is formula of number of subsets with m elements in set with n elements.

$N=\frac{10!}{(10-5)!\times5!}=\frac{10!}{5!\times5!}=\frac{6\times7\times8\times9\times10}{5!}=252;$

Answer:

$N=252$ -number of different committees with 5 people.