Arrangements & Factorials — How Many Orders? (Grades 7–8)
When order matters — like lining people up — count the arrangements (permutations). For the first spot there are n choices, then n−1 for the next, and so on, which is n! ("n factorial"). Three books arrange in 3! = 3 × 2 × 1 = 6 ways; four in 4! = 24.
Understanding arrangements & factorials
When order matters — like lining people up — count the arrangements (permutations). For the first spot there are n choices, then n−1 for the next, and so on, which is n! ("n factorial"). Three books arrange in 3! = 3 × 2 × 1 = 6 ways; four in 4! = 24.
Key Idea
When order matters — like lining people up — count the arrangements (permutations). For the first spot there are n choices, then n−1 for the next, and so on, which is n! ("n factorial"). Three books arrange in 3! = 3 × 2 × 1 = 6 ways; four in 4! = 24.
Seeing it in action
Worked example
How many ways to line up 3 books?
3! = 3 × 2 × 1 = 6.
When order matters, multiply the descending choices.
Try a few
Arrange 4 people in a row
4!.
Arrange 2 items
Arrange 5 books
5!.
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