Question

How do you simplify `""_10P_8`?

Answer 1

`(10!)/(2!)=(10xx9xx8xx7xx6xx5xx4xx3xxcancel2)/cancel2=1,814,400`

Explanation:

The permutation general formula is:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

and so the question is how to calculate:

`P_(10,8)=(10!)/((10-8)!)=(10!)/(2!)`

There are two ways to do it:

• We can look up the values on a chart (I use the one at https://www.mathsisfun.com/numbers/factorial.html), and so `10! = 3,628,800 and 2! = 2`, giving us:

`(3,628,800)/2=1,814,400`

• Or we can show the multiplications:

`(10xx9xx8xx7xx6xx5xx4xx3xxcancel2)/cancel2=1,814,400`