To Calculate a Combination: $_{n}C_r$

The combination function, $ {n}C r$, calculates the number of ways to choose 'r' objects from a set of 'n' objects when the order of selection does not matter. You can easily access this function on a graphing calculator by navigating to the MATH menu and selecting the PRB (Probability) option to solve problems involving unordered groups.

To calculate $ {15}C 7$: Enter 15, press MATH, go to PRB, select 3: $ {n}C r$, enter 7, and press ENTER to get 6,435. To calculate $ {20}C 4$: Enter 20, press MATH, go to PRB, select 3: $ {n}C r$, enter 4, and press ENTER to get 4,845. How many different 4 person teams can be formed from 10 players? Calculate $ {10}C 4$ to find there are 210 possible teams.

Imagine you're picking 3 friends from a group of 14 to go to the movies. It doesn't matter if you pick Alice, then Bob, then Charlie—it's the same group going! The $ {n}C r$ function is perfect for these 'order doesn't matter' scenarios, like picking a committee or a hand of cards. It does the hard work for you.