Question

How do you evaluate P(10,2)?

Answer 1

`P(10,2)=color(green)(90)`

Explanation:

`P(a,b)` (often written `aPb` or `P_b^(a)`
can be evaluated by the formula
`color(white)("XXX")(a!)/((a-b)!)`

In this case
`color(white)("XXX")P(10,2)=(10!)/(8!)=(10xx9cancel(xx8xx7xx...xx1))/(cancel(8xx7xx...xx1))=90`

Looking at it another way:
There are `10` choices for the first element, which leaves `9` choices for the second element;
implying `10xx9=90` ways of making the choices.