Step by step
The question
Question: work out 6 factorial over 3 factorial.
6!3! =
1 Write out top and bottom
We write both factorials out.
6 factorial on top, 3 factorial at the bottom.
6!3! = 6 × 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 cannot divide 6 by 3 first.
We cancel the same numbers.
Careful: not 2! ✗
What is left is 6 × 5 × 4.
6!3! = 6 × 5 × 4
3 Multiply
6 times 5 is 30.
30 times 4 is 120.
6 × 5 = 30
30 × 4 = 120
So it is 120.
6!3! = 120
4 Check
Let's check: 6 factorial is 6 times 5 times 4, times 3 factorial.
6! = 6 × 5 × 4 × 3!
So dividing by 3 factorial leaves 6 times 5 times 4: 120.
So the answer is right!
6! ÷ 3! → 6 × 5 × 4 = 120
Let's look back.
First: write out top and bottom.
Then: cancel.
Then: multiply.
Last: check.
Answer
6!3! = 120