Final answer:
The third baseman can attempt a double play by throwing to second base, get a sure out by throwing to first base, prevent a run by throwing home, or hold the ball to avoid a potential error.
Step-by-step explanation:
When a third baseman fields a ground ball with one out and runners on first and second, he has several options:
- Throw to second base in an attempt to get the lead runner out and possibly turn a double play. This would require a quick throw from the second baseman to first.
- Throw to first base to get the batter out. This is often seen as the safest play to ensure an out.
- Throw home in order to prevent the runner at second base from scoring. This play is riskier and more common in situations where it's essential to keep the game close.
- Hold the ball if none of the other options are viable, avoiding the risk of a throwing error that could allow runners to advance.
Choosing the best option depends on the context of the game, the skill of the runners, and the third baseman's own abilities.