Question

How many ways are there to choose a committee of 5 people from a group of 15 people?

Answer 1

Since order doesn't matter in this problem, we use the combination formula.

Explanation:

The combination formula is: `(n!) / ((n - r)!r!)`, where n is the total number of items (15 in this case) and r is the number of items being selected at once (5 in this case)

Plugging our numbers into the formula we get:

`(15!) / ((15 - 5)!5!)`

After simplifying (very preferably with a scientific or graphing calculator), we get 3003.

So, there are 3003 ways of picking 5 people from a group of 15.

Note that the combination formula can be noted by `_nC_r`. It is this way that you can enter it onto a graphing calculator.

Practice exercises:

1. An earthquake preparation is being prepared. 18 people apply for 3 available jobs. Find the number of distinctive ways of allotting the positions.

Good luck!