Question 427273
A property of combinatorics says that c(N, r) is the same as c(N, N-r). It is easy to prove either algebraically or using a committee-forming argument, since choosing r people on the committee is the same as choosing N-r people *not* on the committee. In addition, C(N, k) = C(N, m) if and only if k+m = N.


Using this property, we can let k = r and m = r+2, and they must add up to 18. Hence,


{{{r + (r+2) = 18}}} --> {{{2r = 16}}} --> r = 8.