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.

Explanation

A)`nC_r`

B)`nC_r=1*1`

C)`n+rC_n=(n+r!)/(n!*r!)`

d)n can be 1 or -1

`(n-1)C_(r-1)+(n-1)C_r=nC_r`.

option C is correct.