# 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 200 students, how many different committees can be...

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 200 students, how many different committees can be formed?

Matthew Fonda | eNotes Employee

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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.