The number of ways of selecting one or more things out of n dissimilar things is

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 number of ways of selecting ' n ' things out of '3n ' things of which 'n ' are of one kind and alike and 'n ' are of second kind and alike and the rest unlike is :

If 'n' things are arranged in circular order, then show that the number of ways of selecting four of the things no two of which are consecutive is (n(n-5)(n-6)(n-7))/(4!)

No. of ways of selecting none or more of 10 identical things is

If n,(n>5) things are arranged in a circular order,the number of ways of selecting three of the things so that no two of which are next to each other is

If the difference of the number of arrangements of three things from a certain number of dissimilar things and the number of selection of the same number of things from them exceeds 100, then the least number of dissimilar things is a.8 b.6 c.5 d.7