Final answer:
The best joining words to use in connecting the provided sentences to indicate contrast and reasoning are 'but' and 'since'.
Step-by-step explanation:
The sentences provided describe a scenario where Americans were underdogs, specifically mentioning they were college students and that their coach believed they could win. To join two of these sentences using conjunctions, you could choose 'but' and 'since' for different contextual meanings. For example, 'The Americans were the underdogs, but their coach thought they could win.' This implies contrast between the underdog status and the coach's belief. Alternatively, 'The Americans were the underdogs, since they were all college students.' Here, 'since' provides a reason for being underdogs.