Question

There are 5 faculty, 4 students, and 3 office staff eligible to serve on a 6-person committee. How many committees are possible containing at most 1 faculty member?

Answer 1

Here, we form a 6 persons committee, there are 5 faculty, 4 students, 3 office staff.
The committee can contain at most one faculty member.

So we can take only one faculty

or no faculty-

If we take one faculty member then-
For the remaining 5 places there are- 4 students, 3 office staff.
the remaining 5 places can be filled in- waysways.
If we take no faculty member then the 6 places can be filled in-waysways

No of possible committees: committees

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