1. Lesson 1

1.5. Expore 4

Mathematics 30-2 Module 3

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

 

In Try This 3, you found that you could calculate the number of ways 10 children could be lined up by finding the product of all consecutive natural numbers less than or equal to 10.

 

In mathematics, there is a short-cut notation for the product of a positive integer, n, and all integers less than or equal to n called factorial notation. It is denoted as n!.

 

Therefore, in Try This 3, students can be lined up in 10! ways.

 

Try This 4

 

To learn more about how factorial notation works, use the interactive piece titled Number of Arrangements to line up 10 students.

 

 

This is a play button for Number of Arrangements.

 

Self-Check 3
  1. What is the value of 5!? Answer
  2. How can 6 × 5 × 4 × 3 × 2 × 1 be written using factorial notation? Answer

 

textbook

  1. Complete questions 5, 6, 7, 9, 11, 15, and 16 on pages 73 to 75 of your textbook. Answer



glossary

Add factorial notation to your copy of Glossary Terms. For each new definition in your glossary, be sure to include the appropriate notation.





formula

Add the following formulas to your copy of Formula Sheet:

  • fundamental counting principle: If there are a ways to perform one task and b ways to perform a second, independent task, then there are a • b ways for performing both tasks.
  • factorial notation: n! = n(n − 1)(n − 2)…(3)(2)(1)