Question

There are 21 mathematic majors and 129 computer science majors at a college. A) How many ways are there to pick 4 representatives, so that 2 is/are mathematics majors and the other 2 is/are computer science majors

Answer 1

Answer: 1,733,760

Explanation:

The number of combinations of selecting m things from n things is given by :-

`^nC_m=(n!)/(m!(n-m)!)`

Given : There are 21 mathematics majors and 129 computer science majors at a college.

Then, the number of ways to pick 4 representatives, so that 2 are mathematics majors and the other 2 are computer science majors :-

`^(21)C_2*^(129)C_2\\\\=(21!)/(2!(21-2)!)*(129!)/(2!(129-2)!)\\\\=(21*20*19!)/(2*19!)*(129*128*127!)/(2*127!)\\\\=210*8256= 1733760`

Hence, the number of ways to pick 4 representatives, so that 2 are mathematics majors and the other 2 are computer science majors =1,733,760