These are pretty straight forward using a little common sense and the "fundamental rule of counting": If one thing can happen innways and another can happen inmways they can happen together innmways.

There are a total of 17 students. You have 17 choices for the first student. Then there remain 16 choices for the second student. So 17(16) ways to do this.

(b) 2 males and 1 female from the classIfwe were to choose the two males first, there would be 10 choices for the first male and 9 choices for the second, then 7 choices for the female so 10(9)(7). However, we do not have to choose in that order. There are 3(2)(1)= 6 orders in which to choose the two males and one female (writing M1 for the one of the males, M2 for the other, and F for the female those 6 orders would be M1M2F, M1FM2, M2M1F, M2FM1, FM1M2, FM2M1) so there are 10(9)(7)(6) ways to do this.

??? How large is the committee? If you mean "form a committee consisting of all the seven females in the class, there would, of course, be one such committee. But I suspect you mean "How many ways to form a committee of "n" people, chosen from the 7 females". To answer that we need to know what "n" is.(c) All females from the class

This is the same as (c) but with males replacing females. How large is the committee to be?(d) No Females

I found this solution that is kind of similar, but I am having trouble understanding it. How do I answer these questions?

Thank you!