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There are 15 players on a soccer team. Only 11 players can be on the field for a game. How many different groups of players of 11 players can the coach make, if the position does not matter?

Sagot :

Given:

There are 15 players on a soccer team.

Only 11 players can be on the field for a game.

We will find the number of groups of players of 11 players can the coach make.

Note: the position does not matter, so, we will use the combinations

We will use the following formula:

[tex]^nC_r=\frac{n!}{(n-r)!*r!}[/tex]

substitute n = 15, and r = 11

[tex]^{15}C_{11}=\frac{15!}{(15-11)!*11!}=\frac{15*14*13*12*11!}{4*3*2*1*11!}=\frac{32760}{24}=1365[/tex]

So, the answer will be:

The number of different groups = 1365

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