Question

Evaluate. 5!4! = [?]

Answer 1

2880

Explanation:

`!` in mathematics means factorial.

What is factorial?

Factorial is the product of an integer and all below it to `1`

`n!` `=n*(n-1)!` for `n≥1` or simply `n!` `=1*2*3*...n`

Notice that `0!` is defined as `1` by mathematicians as it is the empty product.

So for `5!`, we have

`5!` `=5*(5-1)!` `rArr5!` `=5*4!`

`5!` `=5*4*(4-1)!` `rArr5!` `=5*4*3!`

`5!` `=5*4*3*(3-1)!` `rArr5!` `=5*4*3*2!`

`5!` `=5*4*3*2*(2-1)!` `rArr51` `=5*4*3*2*1!`

But, `1!` `=1*(1-1)!`

Which is `1!` `=1*0!` and `0!` `=1`

Finally,

`rArr5!` `=5*4*3*2*1`

That is the pattern, so `n!` `=n*(n-1)!` `...1!` until you get to `1!`

Or simply; `n!` `=1*2*3*...n`

`:.5!4!` `=(5*4*3*2*1)*(4*3*2*1)`

`rArr120*24=2880`