Question

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

• 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 $r$ l's
• C. number of non decreasing 2-D paths from the lattice point $(0,0)$ to $(r,n)$
• D. number of ways of selecting $r$ things out of $n$ different things when a particular thing is always included plus the number of ways of selecting ' $r$ ' things out of $n$, when a particular thing is always excluded

Answer 1

Answer: (A), (B), (D)

Correct answer is (a) number of possible subsets of $r$ members from a set of $n$ distinct members Correct answer is (b) number of possible binary messages of length $n$ with exactly $r$ l's Correct answer is (d) number of ways of selecting $r$ things out of $n$ different things when a particular thing is always included plus the number of ways of selecting ' $r$ ' things out of $n$, when a particular thing is always excluded