The number of values in set of values of `r` for which `^ (23) C_r+2.^(23)C_(r+1)+^(23)C_(r+2)geq^(25)C_(15)` is

The value of r for which .^(20)C_(r ), .^(20)C_(r - 1) .^(20)C_(1) + .^(20)C_(2) + …… + .^(20)C_(0) .^(20)C_(r ) is maximum, is

Prove that ""^(n)C_r + ""^(n)C_(r-1) = ""^(n+1)C_r

The value of sum_(r=0)^(3) ""^(8)C_(r)(""^(5)C_(r+1)-""^(4)C_(r)) is "_____" .

The value of sum_(r=0)^(40) r""^(40)C_(r)""^(30)C_(r) is

Prove that sum_(r=0)^(2n)r(.^(2n)C_r)^2=n^(4n)C_(2n) .

If .^(15)C_(2r-1)=.^(15)C_(2r+4) find r

Find the value (s) of r satisfying the equation "^69 C_(3r-1)-^(69)C_(r^2)=^(69)C_(r^2-1)-^(69)C_(3r)dot

.^((n-1)C_(r) + ^((n-1)) C_((r-1)) is

If .^(15)C_(2r-1) = .^(15)C_(2r + 4) " find " r

The value of sum_(r=0)^(10) (-1)^(r).4^(10-r)""^(30)C_(r)""^(30-r)C_(10-r) is equal to