Question

A committee consisting of 2 faculty members and 4 students is to be formed. Every committee position has the same duties and voting rights. There are 10 faculty members and 11 students eligible to serve on the committee. In how many ways can the committee be formed?

Answer 1

14,850 ways

Explanation:

Since the order does not matter, the number of possible committees is given by the product of the combination of picking 2 out of 10 faculty members and the combination of picking 4 out of 11 students:

`n= (10!)/((10-2)!2!)* (11!)/((11-4)!4!)\\n=(10*9)/(2)*(11*10*9*8)/(4*3*2*1)\\n=14,850`

The committee can be formed in 14,850 ways