# How do you evaluate 12P7?

Feb 16, 2017

${\textcolor{w h i t e}{x}}^{12} {P}_{7} = 3991680$

#### Explanation:

Perhaps you mean ${\textcolor{w h i t e}{x}}^{12} {P}_{7}$, which means

the number of ways one chooses a sample of $7$ objects from a set of $12$ distinct objects, where order does matter and replacements are not allowed .

As color(white)(x)^nP_r=(n!)/((n-r)!)

and hence color(white)(x)^12P_7=(12!)/((12-7)!)

= (12!)/(5!)=(12xx11xx10xx9xx8xx7xx6xx5xx4xx3xx2xx1)/(5xx4xx3xx2xx1)

= $12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 = 3991680$