Question

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

Answer 1

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.