Step by step
The question
Question: work out 10 factorial over 8 factorial.
10!8! =
1 Write out top and bottom
We write both factorials out.
10 factorial on top, 8 factorial at the bottom.
10!8! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 18 × 7 × 6 × 5 × 4 × 3 × 2 × 1
2 Cancel
8 times 7 times 6 times 5 times 4 times 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 10 by 8.
We cancel the numbers that are the same.
Careful: cancel the same numbers
What is left is 10 × 9.
10!8! = 10 × 9
3 Multiply
10 times 9 is 90.
10 × 9 = 90
So it is 90.
10!8! = 90
4 Check
Let's check: 10 factorial is 10 times 9, times 8 factorial.
10! = 10 × 9 × 8!
So dividing by 8 factorial leaves 10 times 9: 90.
So the answer is right!
10! ÷ 8! → 10 × 9 = 90
Let's look back.
First: write out top and bottom.
Then: cancel.
Then: multiply.
Last: check.
Answer
10!8! = 90