EXPLORE has 24 chess players. A team of 6 players, as well as 1 captain, will be chosen out of the 24 chess players (i. e. choose 7 players and then select the captain) How many different selections can be made?

Explanation:

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24 ways to choose a captain

then 23! / (17! x 6!) ways to chose a six-person team.

So the solution is 24 x 23! / (17! x 6!) = 2,422,728.

Or choose a seven person team first, then choose a captain

24! / (17! x 7!) x 7 = 2,422,728.

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