statistics

There are 44 mathematics majors and 163 computer science majors, so there are 207 total majors in the college. There are ${207 \choose 2} = 21,858$ ways to select two representatives from these 207 students, so that one is a mathematics major and the other is a computer science major. This can be explained by the combination formula, which states that the number of combinations of $n$ objects taken $r$ at a time is: $n \choose r = \dfrac{n!}{r!(n-r)!}$. In this case, $n$ = 207 and $r$ = 2, so the number of combinations is $\dfrac{207!}{2!(207-2)!} = 21,858$.