### Home > INT3 > Chapter 10 > Lesson 10.3.2 > Problem 10-165

The Spirit Club recently got a call from the school executive council, asking them to make a committee. They now have 10 volunteers and will need to choose a three-person committee. They need to calculate

_{10}*C*_{3}, the number of possible committees, but they have no calculator with them. Homework Help ✎Al had a thought:

*“I remember that the number of three-person committees you can select from 9 volunteers is 84. This would be the number of committees the tenth volunteer will NOT be on because he or she would be selected from the other nine members.”*How would you calculate this number?*“I also know how many committees the new volunteer WILL be on because I can just add his name to each of the two-member committees I had already selected from 9.”*How many possible committees would include the tenth volunteer?Without using a calculator (and without multiplying or dividing), explain how Al used parts (a) and (b) to calculate

_{10}*C*_{3}.How is this related to Pascal’s Triangle?

_{9}*C*_{3}

_{9}*C*_{2} = ?

Add together your answers from parts (a) and (b).

How do you get from one row to the next when writing out Pascal's Triangle?