Question

Evaluate: a) n!/(n-3)!
b) P(6,4)/4!​

Answer 1

Explanation:

a).

n! is

`n(n - 1)(n - 2)(n - 3)(n - 4).........(1)`

(n-3)! is

`(n - 3)(n - 4)(n - 5)..........(1)`

If we divide the two, everything behind (n-3) will just cancel out so we would be left with only

`(n)(n - 1)(n - 2)`

So the answer to a is

`n(n - 1)(n - 2)`

b

Permutations formula of P(6,4) is

6!/(6-4)!, or 6!/2!.

`(6 * 5 * 4 * 3 * 2 * 1)/(2 * 1) = 360`

Then we divide by 4!

`(360)/(4 * 3 * 2 * 1) = 15`

The answer to b is 15