Factorials – Outschool

Factorials Lesson 

New notation:

6 factorial, written 6!, means 6 • 5 • 4 • 3 • 2 • 1.

Be prepared to expand factorials and simplify.

Example: Evaluate [latex]displaystyle{frac{8!}{5!}}[/latex] .

→   [latex]displaystyle{frac{8 cdot 7 cdot 6 cdot 5 cdot 4 cdot 3 cdot 2 cdot 1}{5 cdot 4 cdot 3 cdot 2 cdot 1}}[/latex]

After cancelling:

→   [latex] 8 cdot 7 cdot 6[/latex]

→   [latex]336[/latex]

Example:  In how many different ways can you arrange the letters of the word VICTORY?

There are 7 options for the first letter. After one letter is chosen, there are 6 options for the second letter. Continuing the same stream of thought, you get:

7 options • 6 options • 5 options • 4 options • 3 options • 2 options • 1 option

→ 7! options

→ 840 options

There are 840 ways the letters of the word VICTORY can be arranged.

Example: In how many different ways can you arrage the letters of the word CANYON?

This is a slightly trickier item because CANYON has 2 Ns.

Take your total number of possible arrangements, 6!, and divide by 2! to acccount for N appearing twice in CANYON.

→ [latex]displaystyle{frac{6!}{2!}}[/latex]

→ [latex]displaystyle{frac{6 cdot 5 cdot 4 cdot 3 cdot 2 cdot 1}{2 cdot 1}}[/latex]

→ [latex]6 cdot 5 cdot 4 cdot 3[/latex]

→ [latex]360[/latex]

There are 360 different possible arrangements of CANYON.

Factorials Quiz