Posted by kitkat on Saturday, November 27, 2010 at 10:01pm.
In Lisa's firstyear 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?

math 12  Reiny, Saturday, November 27, 2010 at 11:12pm
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 
math 12  Anonymous, Sunday, November 28, 2010 at 10:37am
Thank you:) I got that answer too:)

math 12  qwenie, Wednesday, March 23, 2016 at 6:32pm
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?