Question

How do you write `12 times 11 times 10 times 9 times 8 times 7 times 6` using factorials?

Answer 1

see below

Explanation:

`12!` is `12 * 11 * 10... * 2 * 1`

`5!` is `5 * 4 * 3 * 2 * 1`

`12! / 5! = (12 * 11 * 10 * ... * 1)/(5 * 4 * 3 * 2 * 1)`

simplifying the fraction (by cancelling out `5 * 4 * 3 * 2 * 1`) gives

`(12 * 11 * 10 * 9 * 8 * 7 * 6) / 1` or `12 * 11 * 10 * 9 * 8 * 7 * 6`.