Lesson 2
1. Lesson 2
1.5. Explore
Module 3: Permutations, Combinations, and the Fundamental Counting Principle
Explore
In Try This 1, you discovered that n! can be written several ways. One general expression you may have found is n! = n(n − 1)!. In the following Try This, you will see some other ways to write n!.
Try This 2
Most scientific calculators have a factorial key that will calculate the product of the consecutive natural numbers beginning with the number entered. Simply enter the number and press the ! key. Some graphing calculators do not have a factorial key but have the factorial function listed within the menu system. You may need to consult your calculator instructions or your teacher to find where the ! function is located.
- Using your calculator, evaluate the following expressions.
- 6!
- 6 × 5!
- 6 × 5 × 4!
- What do you notice about your answers for questions 1.a., b., and c.?
Save your responses in your course folder.
Self-Check 1
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Rewrite 12! in two different forms. AnswerDid You Know?
Most calculators will have a factorial key, and usually the largest value that can be calculated is 69!. Try 69! in your calculator, and see what happens when you try to enter 70!. - Rewrite 7 × 6 × 5! in two different forms. Answer
There are times when it is necessary to simplify factorial expressions. You will explore one way in the next Try This.
Try This 3
Find the value of 
.
- Expand the numerator to show all the factors in 12!.
- Expand the denominator to show all the factors in 9!.
- Divide the numerator and denominator by any common factors.
- Calculate the solution by multiplying the remaining factors.
Save your responses in your course folder.