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A college has 10 basketball players. A 5 member’s team and a captain will be selected out of these 10 players. How many different selections can be made?

a) 1260
b) 210
c) 10C6 × 6!
d) 10C5 × 6

Answer: a
Explanation: A 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

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