How do you evaluate P(10,2)?

1 Answer
Alan P.
Aug 1, 2016

#P(10,2)=color(green)(90)#

Explanation:

#P(a,b)# (often written #aPb# 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 #10xx9=90# ways of making the choices.

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