Question

How do you simplify `(12!)/(8!4!)`?

Answer 1

495

Explanation:

Remember that a factorial (written with the "!" notation) means to multiply all the natural numbers (1, 2, 3,...) up to and including the number listed. So `(4!)=1xx2xx3xx4`

If I had `(4!)/(3!)`, that'd the same as

`(4xx3xx2xx1)/(3xx2xx1)`. But we can also rewrite this as:

`(4xx3!)/(3!)` and so can cancel out the `3!` and end up with 4.

In the above question, we have

`(12!)/(8!4!)` which I can rewrite as:

`(12xx11xx10xx9xx8!)/(8!4!)` and so can cancel the `8!`:

`(12xx11xx10xx9)/(4!)` and if I expand the `4!` we get:

`(12xx11xx10xx9)/(4xx3xx2xx1)` and we can cancel out some stuff:

`(cancel(12)xx11xxcancel(10)color(red)(5)xx9)/(cancel(4xx3)xxcancel(2)xx1)` and cleaning it up we have:

`11xx5xx9=495`