=(n!)/(r!(n-r)!)

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

The least value of natural number n such that ((n-1),(5))+((n-1),(6))lt((n),(r))," where"((n),(r))=(n!)/((n-r)!r!),is

(ii) (n!)/((n-r)!r!)+(n!)/((n-r+1)!(r-1)!)=((n+1)!)/(r!(n-r+1)!)

Let n and r be non negative integers such that 1<=r<=n* Then,^(n)C_(r)=(n)/(r)*^(n-1)C_(r-1)

Verify that ""^(n)C_(r )=(n)/(r ) ""^(n-1)C_(r-1) where n=6 and r=3 .

If ""^(n)P_(r)=""^(n)P_((r+1)) and ""^(n)C_(r) = ""^(n)C_(r-1), then (n,r) =

"^(n)C_(r)=^(n)C_(n-r)