Step by step
The question
Question: work out 5 factorial over 3 factorial.
5!3! =
1 Write out top and bottom
We write both factorials out.
5 factorial on top, 3 factorial at the bottom.
5!3! = 5 × 4 × 3 × 2 × 13 × 2 × 1
2 Cancel
3 times 2 times 1 is on top and at the bottom.
A top and a bottom divided by the same number: they cancel.
Careful!
We never divide 5 by 3.
We cancel the numbers that are the same.
Careful: cancel the same numbers
What is left is 5 × 4.
5!3! = 5 × 4
3 Multiply
5 times 4 is 20.
5 × 4 = 20
So it is 20.
5!3! = 20
4 Check
Let's check: 5 factorial is 5 times 4, times 3 factorial.
5! = 5 × 4 × 3!
So dividing by 3 factorial leaves 5 times 4: 20.
So the answer is right!
5! ÷ 3! → 5 × 4 = 20
Let's look back.
First: write out top and bottom.
Then: cancel.
Then: multiply.
Last: check.
Answer
5!3! = 20