Problem Page A committee consisting of faculty members and students is to be formed. Every committee position has the same duties and voting rights. There are faculty members and students eligible to serve on the committee. In how many ways can the committee be formed?

This problem can be solved using combinations, because from a group of people, they want to rearrange into a committee, such that it has no restrictions, and there's no specific order to form it.

So, a represents de number of faculty members and b represents the number of students; c is gonna represent the number of people the committee has to have. Just see that the total number of people is a + b.

Then, using Combination formula, which is: [tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]

In the formula, n represents the total number of people, r represents the total number of selected people to form the committee.

So, applying the formula to the problem, variables would be:

n = a + b; r = c.

Hence, [tex]C(a+b,c)=\frac{(a+b)!}{c!((a+b)-c)!}[/tex]

Notice that the result is not a specific number, that is because the problem is general, it doesn't give specific number of people.