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A basketball team has 13 Active players, in how many ways can 5 players be selected to start the game??

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Answer:

1287

Step-by-step explanation:

The number of distinct ways n objects can b selected from N total objects is given by


(N!)/(n!(N-n)!)

Now in our case, we have a total of 13 basketball players. N = 13 and 5 players to choose n = 5. Therefore, the above formula gives


(13!)/(5!(13-5)!)
-(13!)/(5!8!)
=(13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)/(5!\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)
=(13\cdot12\cdot11\cdot10)/(5!)
=(13\cdot12\cdot11\cdot10)/(5\cdot4\cdot3\cdot2\cdot1)
=1287

Hence, there are 1287 ways 5 different players can be selected from 13 players.

User Thitami
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