<p>In a volleyball league with 4 teams, each team plays exactly 2 games with each of the other 3 teams in the league. What is the total numbers of games played in this league? </p>
<p>The answer is 12... why? I thought the answer was 24.</p>
<p>(1 vs 2, 1 vs 3, 1 vs 4, 2 vs 3, 2 vs 4, 4 vs 3) = 6 possibilities
6 * 2 = 12</p>
<p>If you just multiply 4<em>3</em>2, you double-count each game. For example, you count the first 1-vs.-2 as a game for team 1, and then count it again as a game for team 2. But it’s only one game. To undo the double-counting, you need to divide the product by 2.</p>