Factorial recall sprint

Recall single-digit factorials (1! through 6!).

A fluency sprint: build the speed and accuracy you need to do this calculation instantly on test day.

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What to memorize: factorials

\(n!\) ("n factorial") means: multiply every whole number from \(n\) down to 1. \(4! = 4 \times 3 \times 2 \times 1 = 24\).

Memorize these:

Build each one from the one before: \(7! = 7 \times 6! = 7 \times 720 = 5040\).

Why it matters: the number of ways to arrange \(n\) different things in a row is \(n!\). Three books on a shelf can go in \(3! = 6\) orders.

Cancel before you multiply when one factorial divides another: \(\frac{7!}{5!} = 7 \times 6 = 42\).

Common slips: squaring (\(5^2 = 25\)) or multiplying only two numbers (\(5 \times 4 = 20\)) instead of multiplying all the way down to 1, and thinking \(0! = 0\).

Worked examples

Example 1.
\(6! = \)?
Show answer and explanation
Answer:
B

\(6! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 = 720\).

Example 2.
How many different ways can you arrange 5 distinct trophies in a row?
Show answer and explanation
Answer:
D

Arranging 5 distinct items in order has \(5!\) possibilities: \(5! = 120\).

Example 3.
How many different ways can you arrange 4 distinct seashells in a row?
Show answer and explanation
Answer:
C

Arranging 4 distinct items in order has \(4!\) possibilities: \(4! = 24\).