Prove that` n(n -1)(n -2)...... (n-r + 1) = ( n!)/(n-r)!`

Prove that: (i) (n!)/(r!) = n(n-1) (n-2)......(r+1) (ii) (n-r+1). (n!)/((n-r+1)!) = (n!)/((n-r)!)

Prove that: (i) (n!)/(r!) = n(n-1) (n-2)......(r+1) (ii) (n-r+1). (n!)/((n-r+1)!) = (n!)/((n-r)!)

Prove that : (i) (n!)/(r!)=n(n-1)(n-2)...(r+1) (ii) (n-r+1)*(n!)/((n-r+1)!)=(n!)/((n-r)!) (iii) (n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!)=((n+1)!)/(r!(n-r+1)!)

Prove that (n-r+1)((n!)/((n-r+1)!))=((n!)/((n-r)!))

Prove that (n!)/(r!)=n(n-1)(n-2)dots(r+1)

Prove that ((n-1)!)/((n-r-1)!)+r.((n-1)!)/((n-r)!)=(n!)/((n-r)!)

Prove that C(n,r)+C(n-1,r)+C(n-2,r)+......+C(r,r)=C(n+1,r+1)

Prove that n.^(n-1)C_(r-1)=(n-r-1) ^nC_(r-1)

Prove that (n-r+1)(n!)/((n-r+1)!)=(n!)/((n-r)!)

Prove that (n-r+1)(n!)/((n-r+1)!)=(n!)/((n-r)!)