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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