Using the combination formula, the coach can make 5,005 different groups.
The position does not matter, hence the combination formula is used.
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 6 students are taken from a set of 15, hence the number of groups is:
[tex]C_{15,6} = \frac{15!}{6!9!} = 5005[/tex]
More can be learned about the combination formula at https://brainly.com/question/25821700
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