Answer: 1,733,760
Step-by-step explanation:
The number of combinations of selecting m things from n things is given by :-
[tex]^nC_m=\dfrac{n!}{m!(n-m)!}[/tex]
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 :-
[tex]^{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[/tex]
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
