How do you simplify $\frac{(n - 1)!}{n!}$ $((n-1)!) /( n!)$ ?

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Answer 1 · 2015-12-03T18:05:57

Answer: $\frac{1}{n}$ $1/n$

Factorial mean multiply the all the number by counting down...

$\frac{(n - 1)!}{n!} = \frac{(n - 1) (n - 2) (n - 3)!}{(n) (n - 1) (n - 2) (n - 3)!}$ $((n-1)!)/(n!) = [(n-1)(n-2)(n-3)!]/((n)(n-1)(n-2)(n-3)!$

$= [cancel((n-1)(n-2)(n-3)!)]/((n)cancel((n-1)(n-2)(n-3)!)$

= $1/n$

How do you simplify ((n-1)!) /( n!) (n−1)!n!((n-1)!) /( n!) ?