Step by step
The question
Question: work out 6 factorial over 4 factorial.
6!4! =
1 Write out top and bottom
We write both factorials out.
6 factorial on top, 4 factorial at the bottom.
6!4! = 6 × 5 × 4 × 3 × 2 × 14 × 3 × 2 × 1
2 Cancel
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 6 by 4.
We cancel the numbers that are the same.
Careful: cancel the same numbers
What is left is 6 × 5.
6!4! = 6 × 5
3 Multiply
6 times 5 is 30.
6 × 5 = 30
So it is 30.
6!4! = 30
4 Check
Let's check: 6 factorial is 6 times 5, times 4 factorial.
6! = 6 × 5 × 4!
So dividing by 4 factorial leaves 6 times 5: 30.
So the answer is right!
6! ÷ 4! → 6 × 5 = 30
Let's look back.
First: write out top and bottom.
Then: cancel.
Then: multiply.
Last: check.
Answer
6!4! = 30