Question

There are 18 mathematics majors and 325 computer science majors at a college.
a) In how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major?
b) In how many ways can one representative be picked who is either a mathematics major or a computer science major?

Answer 1

Answer a)

1 representative from a mathematics major and 1 from computer science major can be picked by using the formula 18C1*325C1

= $\frac {18!*325!}{(18-1)!*1!*(325-1)!*1!}=18*325 = 5850 \ ways$

Answer b)

1 representative from a mathematics major or 1 from computer science major can be picked by using the formula 18C1+325C1

$\frac {18!}{(18-1)!*1!}+\frac {325!}{(325-1)!*1!}=18+325 = 343\ ways$