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Q: What is the probability a captain and a goalkeeper will be among 5 players selected from eleven?

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Explanatory AnswerA team of 6 members has to be selected from the 10 players. This can be done in 10C6 or 210 ways.Now, the captain can be selected from these 6 players in 6 ways.Therefore, total ways the selection can be made is 210*6 = 1260.Alternatively, we can select the 5 member team out of the 10 in 10C5 ways = 252 ways.The captain can be selected from amongst the remaining 5 players in 5 ways.Therefore, total ways the selection of 5 players and a captain can be made = 252*5 = 1260.

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