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The passage has already told us that there's a limit of 3 people if the graduation is relocated to the gym on account of rain. So as long as it rains (which C suggests it will), the argument is very solid. The only remaining issue would be whether he can get additional tickets, perhaps by getting some unused tickets from a friend. So C very clearly strengthens the argument by filling in the main conditional: If rain, then relocate.

B, on the other hand, is weird. First, it doesn't give us any reason to believe that the graduation actually will be in the gym. And as we've covered, if that does happen, he's already limited to 3. So why does it matter if he's missing one of the 3? This would just mean that he's actually limited to 2, but it wouldn't give us any additional reason to believe that only 3 people can attend. Toss B out.
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