[" 8.Prove that "],[qquad " (i) "(n!)/(r!)=n(n-1)(n-2)...(r+1)]

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: (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 (n!)/(r!)=n(n-1)(n-2)dots(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)!)

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

Prove that: (i) r.^(n)C_(r) =(n-r+1).^(n)C_(r-1) (ii) n.^(n-1)C_(r-1) = (n-r+1) .^(n)C_(r-1) (iii) .^(n)C_(r)+ 2.^(n)C_(r-1) +^(n)C_(r-2) =^(n+2)C_(r) (iv) .^(4n)C_(2n): .^(2n)C_(n) = (1.3.5...(4n-1))/({1.3.5..(2n-1)}^(2))

Prove that: (i) (.^(n)P_(r))/(.^(n)P_(r-2)) = (n-r+1) (n-r+2)

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