Exercise 36 Page 510

We have a set of 6 people and must choose 4 of them. Since the order in which the players are chosen does not matter, we want to calculate the number of combinations. To do that, we can use the following formula. _nC_r=_nP_r/r! ⇔ _nC_r=n!/(n-r)!r! We have six players to choose from and want to create a group of four. Therefore, we have n= 6 and r= 4.

There are 15 ways we can pick the team if order does not matter.

Alternative Solution

Using a Graphing Calculator

To calculate the number of combinations we can also use the built in combinations formula on our graphing calculator. We start by entering the number of players, which is 6.

Next, push the MATH button, scroll to PRB and choose the third option. Having chosen nCr, we finish by entering the number of people on the team, which is 4.

Note that we obtained exactly the same result as when calculating by using the formula for the number of combinations.