In Lisa's first-year college program she must take nine courses including at least two science courses. If there are five science courses, three mathematics courses, four language courses and five business courses from which to choose, how many different academic programs could she follow?

Answer 1

Without any restrictions she could take
C(17,9) different combinations or 24310

At least 2 science courses means we have to excluse
1. no science course
2. 1 science course

1. number of ways to take no science = C(5,0)xC(12,9)
= 220
2. number of ways to include 1 science course
= C(5,1)xC(12,8)
= 2475

number of ways with at least 2 science courses
= 24310 - 220 - 2475
= 21615

or

2 science courses: C(5,2)xC(12,7) = 7920
3 science courses : C(5,3)xC(12,6) = 9240
4 science courses : C(5,4)xC(12,5) = 3960
5 science courses: C(5,5)xC(12,4) = 495
Total = 21615

Answer 2

Thank you:) I got that answer too:)

Answer 3

There are 20 people in a club. In how many ways can the club elect a president, a secretary and a treasurer, on person can hold more than one office?