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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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