How do you simplify ((a-2)!) / (a!)?

1 Answer
Alan P.
Nov 20, 2015

((a-2)!)/(a!) = 1/(a^2-a)

Explanation:

((a-2)!)/(a!)

color(white)("XXX")= ((a-2)xx(a-3)xx...xx(1))/((a)xx(a-1)xx(a-2)xx(a-3)xx...xx(1))

color(white)("XXX")= (cancel((a-2))xxcancel((a-3))xx...xxcancel((1)))/((a)xx(a-1)xxcancel((a-2))xxcancel((a-3))xx...xxcancel((1)))

color(white)("XXX")=1/(axx(a-1))

color(white)("XXX") = 1/(a^2-a)

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