How do you evaluate the following expression #""^(10)P_(6)#?

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Answer 1 · 2017-06-04T08:22:15

#151,200#

The formula for evaluating a permutation #""^(n) P _(r)# is #frac(n!)((n - r)!)#:

#Rightarrow ""^(10) P _(6) = frac(10!)((10 - 6)!)#

#Rightarrow ""^(10) P _(6) = frac(10!)(4!)#

#Rightarrow ""^(10) P _(6) = 10 times 9 times 8 times 7 times 6 times 5#

#Rightarrow ""^(10) P _(6) = 90 times 56 times 30#

#Rightarrow ""^(10) P _(6) = 90 times 1680#

#therefore ""^(10) P _(6) = 151,200#