A basketball team has 11 players on its roster. Only 5 players can be on the court at one time. How many different groups of 5 players can the team put on the floor?

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Answer 1 · 2016-06-19T19:59:23

55 440 different groups of 5 players.

While there is a formula for choosing so many out of so many, it is easy to work out a question like this by reasoning.

Lets' choose our 5 players one at a time....

For the first player there are 11 players to choose from:

Number of choices = $11$ $11$

For the second player, there are now 10 players to choose from.

Number of choices = $11 \times 10$ $11 xx 10$

IN the same way for the third, fourth and fifth players there are 9,8 and 7 players respectively to choose from.

Number of choices = $11 \times 10 \times 9 \times 8 \times 7$ $11 xx 10 xx 9 xx 8 xx 7$

Total number of possible teams = $55440$ $55 440$