Question

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

Answer 1

`((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)`