Additional mathematics

Question

The committee of a school cooperative consists of 8 members. The committee is chosen from 10 teachers, and 4 students. How many committee can be formed so that each committee consists of 

 

i) 5 teachers

ii) not more than 2 students

Answer 1

1)  10C5•4C3 represents choosingf 5 teachers, from ten, and 3 students, from 4

 

2)  Do similarly to the above, except you must add 3 cases: one when all the committee is teachers, one when exactly one student is chosen, and the last one when exactly two students are selected.  You will have three terms to add up, each structured as I showed in #1 above, with the total chosen being 8 in each case.