Question

from 7 professors and 10 students,a committee of 5 is to be formed. in how many ways can this be done if the committee contains exactly 3 professors

Answer 1

Answer:

Explanation:

There are a total of 17 persons (7 professors + 10 students) from which a committee of 5 is to be formed. This can be done in 10C5 ways.

The number of ways that a committee can be formed with no students in it is to select 5 teachers out of the pool of 17 professors available. This can be done in 6C5 ways.

Therefore the total number of ways that the committee can be formed with at least one student in it is 10C5 - 6C5.

10C5 = 252

6C5 = 6

Therefore the required number of ways = 246

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