# Average number, combinatorics

• November 30th 2012, 02:17 AM
wilhelm
Average number, combinatorics

1. Nine boys and fourteen girls are arranged in a row in all possible ways. What is the average number of "neighbours" of opposite sex.

2. Consider a family of all $k$-element subsets of a set $\left\{ 1,2,......,2n\right\}$. For every such set consider its smallest element. Find the average value of the smallest element in all $k$-element subsets.