Question

A student-faculty committee consisting of 6 members is to be chosen from a pool of candidates consisting of 5 students and 7 faculty members. The committee must have at least 2 student members and at least 1 faculty member. How many possibilities are there

Answer 1

`T=812`

Explanation:

From the question we are told that:

No. Committee Members
`n=6`

Pool of : 5 students and 7 faculty members

At least 2 student members and at least 1 faculty member

Generally the committee is mathematically given by

The Total Events are

`T=(^5C_2*^7C_4)+(^5C_3)*(^7C_3)+(^5C_4)*(^7C_2)+(^5C_5)*(^7C_1)`

`T=350+350+105+7`

`T=812`