Question

How do you evaluate 12P7?

Answer 1

`color(white)(x)^12P_7=3991680`

Explanation:

Perhaps you mean `color(white)(x)^12P_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)`

= `12xx11xx10xx9xx8xx7xx6=3991680`