Question

how many committees of four can be chosen from twelve students?

how many of these will include a given student?

how many will exclude a given student?

Answer 1

you are being asked for the number of ways to choose 4 from 12, written as
\[\dbinom{12}{4}\] read "12 choose 4" and computed via
\[\dbinom{12}{4}=\frac{12\times 11\times 10\times 9}{4\times 3\times 2}\] cancel first, multiply last

Answer 2

what about the last two question?

Answer 3

I don't understand what the last two questions are asking for