A university undergraduate has to take 5 courses from a pool of 4 mathematics and 3 physics courses. In how many ways can he select his courses so that he takes exactly two courses in physics?

Answer 1

so he takes 2 of the 3 physics courses and 3 of the 4 math courses
C(3,2) x C(4,3)
= 3(4) or 12 ways

second interpretation: he takes 2 specific physics courses which would be 1 way, then he needs 3 more courses of the remaining 5.
= 1 x C(5,3) = 10