Evaluate `(n !)/(r !(n-r)!)`, when n = 5, r = 2.

Evaluate (n !)/((n-r)!), when (i) n = 6, r = 2 (ii) n = 9, r = 5

Evaluate (n!)/(r!(n-r)!) , where n=15,r=4

Evaluate : (n!)/((n-r)!) where n=5,r=2

Evaluate: sum_(r=1)^n(3^r-2^r)

If n = 12, r = 4 , then evaluate the following: (i) (n!)/(r!(n-r)!) (ii) (n!)/((n-r+2)!)

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

T_(n) =sum _( r =2n )^(3n-1) (r)/(r ^(2) +n ^(2)), S_(n) = sum _(r =2n+1)^(3n) (r )/(r ^(2) + n ^(2)), then AA n in {1,2,3...}:

If sum _(r =1) ^(n ) T _(r) = (n +1) ( n +2) ( n +3) then find sum _( r =1) ^(n) (1)/(T _(r))

Statement-1 : The expression n!(100 - n)! is maximum when n = 50 . Statement-2 : .^(2n)C_(r) is maximum when r = n .

Find the sum sum_(r=1)^n r/((r+1)!) where n!= 1xx2xx3....n .