Question

Show that (n,(n-2))= (n(n-1))/2
**note that (n, (n-2)) is not an ordered pair/relation. It is written as n on top of (n-2). Like in permutation format

Answer 1

\[\binom n{n-2}=\frac{n!}{(n-2)!(n-(n-2))!}=\frac{n!}{2!(n-2)!}\]

Answer 2

Either simplify from there, or you can try a more interesting approach involving the binomial theorem.

Answer 3

is that just using the definition of factorials??
like n(n-1)(n-2)...(2)(1)??

Answer 4

Yes

Answer 5

thank you I will try that

Answer 6

yw

Answer 7

How would I write (n-2)!?
Is it (n-2)(n-3)...(2)(1)

Answer 8

You don't need to expand that factorial. In the numerator, you have \(n!=n(n-1)(n-2)!\), and this factor of \((n-2)!\) will cancel with the \((n-2)!\) in the denominator.