How do you evaluate 12P7?

1 Answer
Feb 16, 2017

Answer:

#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#