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

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=

""^(n)C_(r+1)+^(n)C_(r-1)+2.""^(n)C_(r)=

""^(n) C_(r+1)+2""^(n)C_(r) +""^(n)C_(r-1)=

The number of values of 'r' satisfying the equation ""^(39)C_(3r-1)- ""^(39)C_(r^(2) )= ""^(39)C_(r^(2)-1) - ""^(39)C_(3r) is

If m, n, r, in N then .^(m)C_(0).^(n)C_(r) + .^(m)C_(1).^(n)C_(r-1)+"…….."+.^(m)C_(r).^(n)C_(0) = coefficient of x^(r) in (1+x)^(m)(1+x)^(n) = coefficient of x^(f) in (1+x)^(m+n) The value of r for which S = .^(20)C_(r.).^(10)C_(0)+.^(20)C_(r-1).^(10)C_(1)+"........".^(20)C_(0).^(10)C_(r) is maximum can not be

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

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

For ""^(n) C_(r) + 2 ""^(n) C_(r-1) + ""^(n) C_(r-2) =

""^(n-2)C_(r)+2""^(n-2)C_(r-1)+""^(n-2)C_(r-2) equals :