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

Step-by-step explanation:

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

$^nC_m=\dfrac{n!}{m!(n-m)!}$

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 :-

$^{21}C_2\times^{129}C_2\\\\=\dfrac{21!}{2!(21-2)!}\times\dfrac{129!}{2!(129-2)!}\\\\=\dfrac{21\times20\times19!}{2\times19!}\times\dfrac{129\times128\times127!}{2\times127!}\\\\=210\times8256= 1733760$

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