# How do you evaluate P(10,2)?

Aug 1, 2016

$P \left(10 , 2\right) = \textcolor{g r e e n}{90}$

#### Explanation:

$P \left(a , b\right)$ (often written $a P b$ 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 $10 \times 9 = 90$ ways of making the choices.