A student planning her curriculum.. must select 1 of 5 business courses, 1 of 5 math courses, 2 of 12 elective courses, and either 1 of 4 history courses or one of five social science courses.

Question

A student planning her curriculum for the upcoming year must select one of five business courses, one of five mathematics courses, two of twelve elective courses, and either one of four history courses or one of five social science courses. How many different curricula are available for her consideration?

Answer 1

We need to find out the combinations of classes. C(n,r) = n!/(n-r)!r! (pick r out of n)

1 out of 5 business classes = 5!/(5-1)!1! = 5!/4! = 5

1 out of 5 math = 5

2 out of 12 elective = 12!/(10! 2!) = 12*11/2 = 66

These three will make 5*5*66 combinations

Either one of

1 out of 4 history = 4

1 out of 5 social science = 5

(5*5*66)*4 + (5*5*66)*5 = 5*5*66*9 = 14850