How do I solve the following problem? Thanks!A principal wants to make a committee of four teachers and six students. If there are 22 teachers and...

To solve this problem, there is a rule sometimes referred
to as The Fundamental Principle of Counting. It states that if some
event can be broken down into subevents, then the total number of ways the event can
occur is the product of the numbers of ways the subevents can
occur.

By applying this principle, it follows that our
answer will be (number of ways to pick four teachers) * (number of ways to pick six
students).

To count these numbers, we use combinations. For
teachers, we must choose 4 from 22, and students we must choose 6 from 200. Thus our
answer is:

Total different committees
= `((22),(4))((200),(6))`

The above is a very large number,
so the above is what I would report as the "answer." If you wish to evaluate it, it
comes out to 602,819,101,384,500 possible
committees.