<p>What is the average number of pairs of consecutive integers in a randomly selected subset of <img alt="$5$" height="12" src="https://latex.artofproblemsolving.com/7/9/0/79069377f91364c2f87a64e5f9f562a091c8a6c1.png" width="8" /> distinct integers chosen from the set <img alt="$\{ 1, 2, 3, …, 30\}$" height="20" src="https://latex.artofproblemsolving.com/f/c/7/fc70ac2f15c624633215553837b13ac3230b80e1.png" width="121" />? (For example the set <img alt="$\{1, 17, 18, 19, 30\}$" height="20" src="https://latex.artofproblemsolving.com/5/b/f/5bfe9b6e9825a7b2841ba88fb287c4e1a5088931.png" width="134" /> has <img alt="$2$" height="12" src="https://latex.artofproblemsolving.com/4/1/c/41c544263a265ff15498ee45f7392c5f86c6d151.png" width="8" /> pairs of consecutive integers.) The result will count 2 digits after the dot.</p>

Question No: 434

What is the average number of pairs of consecutive integers in a randomly selected subset of $5$ distinct integers chosen from the set $\{ 1, 2, 3, …, 30\}$ ? (For example the set $\{1, 17, 18, 19, 30\}$ has $2$ pairs of consecutive integers.) The result will count 2 digits after the dot.

Editorial

Tags: Combinatorics Probability

Question Details