The combinatorial coefficient C(n, r) is equal to

The combinatorial coefficient C(n, r) can not be equal to the (A) number of possible subsets of r members from a set of n distinct members. (B) number of possible binary messages of length n with exactly r 1's. (C) number of non decreasing 2-D paths from the lattice point (0,0) to (r, n) (D) number selecting r things out of n different things when a particular thing is always included plus of ways of the number of ways of selecting r things out of n, when a particular thing is always excluded.

The combinatorial coefficients ""^(n – 1)C_(p) denotes

The combinatorial coefficients ""^(n – 1)C_(p) denotes

Statement-1 : The sum of the series ^nC_0. ^mC_r+^nC_1.^mC_(r-1)+^nC_2.^mC_(r-2)+......+^nC_r.^mC_0 is equal to ^(n+m)C_r, where C's and C's denotes the combinatorial coefficients in the expansion of (1 + x)^n and (1 + x)^m respectively, Statement-2: Number of ways in which r children can be selected out of (n + m) children consisting of n boys and m girls if each selection may consist of any number of boys and girls is equal to ^(n+m)C_r

Middle Terms || Sum OF Coefficient and Sum OF Combinatorial Coefficient and Theory OF Numerically Greatest Term

Middle Terms || Sum OF Coefficient || Sum OF Combinatorial Coefficient || Theory OF Numerically Greatest Term

If ""(n)C_(0), ""(n)C_(1), ""(n)C_(2), ...., ""(n)C_(n), denote the binomial coefficients in the expansion of (1 + x)^(n) and p + q =1 sum_(r=0)^(n) r^(2 " "^n)C_(r) p^(r) q^(n-r) = .

If ""(n)C_(0), ""(n)C_(1), ""(n)C_(2), ...., ""(n)C_(n), denote the binomial coefficients in the expansion of (1 + x)^(n) and p + q =1 sum_(r=0)^(n) r^(2 " "^n)C_(r) p^(r) q^(n-r) = .