Question

What is `(5!3!)/(6!)`?

Answer 1

`1`

Explanation:

This problem can be made easier by rewriting the equation:

`(5 * 4 * 3 * 2 * 1 * 3 * 2 * 1)/( 6 * 5 * 4 * 3 * 2 * 1)`

We can cancel quite a few numbers:

`(cancel(5 * 4 * 3 * 2 * 1) * 3 * 2 * 1)/( 6 * cancel(5 * 4 * 3 * 2 * 1)`

`(3 * 2 * 1)/6`

`6/6 = 1`

Answer 2

The answer is `1`.

Explanation:

The ! is a factorial, which means if you have, for example, `4!`, you just do `4*3*2*1=24`.

Method 1:

Multiply the `6!` out to be `6*5!` and get `(5!3!)/(6*5!)`.
(We do this so we can cancel out the `5!`s in the next step.)
Cancel out the `5!`s and get: `(3!)/6`
Now just multiply out the `3!` to be `3*2*1=6`.
You end up with `6/6`, which equals `1`.

This looks like a lot, but it's actually quite nice because you don't have to multiply out the `5!` or `6!` completely.

Method 2:

Another way to do this is just completely multiply everything out like this:
`(5*4*3*2*1*3*2*1)/(6*5*4*3*2*1)`
Cancel everything out that you can, and you should end up with the same answer, `1`.