1. Lesson 4

1.7. Explore 3

Mathematics 30-2 Module 3

Module 3: Permutations, Combinations, and the Fundamental Counting Principle

 

So far, you have seen that  can be used to determine the number of combinations. It is also possible to rewrite this formula without the permutation component.

 

 

So it is easier to visualize, rewrite the division by r! as the multiplication by

    

Since you know that nPr can be written as you can then replace nPr with to make solving the question easier.

Multiply.

 

So the combination formula is as follows:

 

 



textbook

This photo shows a coach talking with a young girls’ basketball team.

Brand X Pictures/Thinkstock

Read “Example 2” on page 113 of your textbook. Notice how 10! is rewritten in the numerator as 10 × 9 × 8 × 7! so that the common factor, 7!, can be divided out of both the numerator and denominator.

 

Self-Check 2
  1. Complete “Your Turn” on the bottom of page 113 of your textbook. Answer
  2. In how many ways can a coach choose a starting line-up of 5 basketball players if there are 15 players on the team? Answer
Did You Know?


This is a photo of a combination lock.

iStockphoto/Thinkstock

Have you ever had a combination lock given to you for a locker at school? Is this an appropriate name for this item? The word combination implies that order is not important. You know, however, that if the numbers are not done in the right order with the correct rotation in between, the lock will not unlock. So perhaps it should be called a permutation lock.