Final answer:
To compare the number of games required for a twelve-team volleyball tournament played in one pool versus two pools, we use the round-robin formula n(n - 1) / 2. In one pool of twelve, 66 games are needed; split into two pools of six, only 30 games in total are required.
Step-by-step explanation:
The question asks to compare the number of games required when a twelve-team pool is split into two pools of six for a volleyball tournament. To determine the number of games in each scenario, we can use a common formula for round-robin tournaments, which is n(n - 1) / 2, where n is the number of teams in the pool. If all teams in a single pool of twelve play each other once, the formula gives us 12(11) / 2 = 66 games. When split into two pools of six, each pool would require 6(5) / 2 = 15 games, so together, the two pools would require 30 games in total. Thus, splitting the pool into two results in fewer games (30) compared to having one pool of twelve (66 games).