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Answer :
315$ ways 7 soccer balls be divided among 3 coaches for practice.
There are several ways of solving this type of problem. Here, we will employ the stars-and-bars approach: using a specific number of dividers (bars) to divide a specific number of objects (stars) into groups, where each group can contain any number of objects.
However, the first thing to consider when employing this method is the number of dividers (bars) required.
The number of dividers required in this problem is two.
The first coach will receive the soccer balls to the left of the first divider (bar), the second coach will receive the soccer balls between the two dividers (bars), and the third coach will receive the soccer balls to the right of the second divider (bar).
Thus, we need two dividers and seven stars. Therefore, we have seven stars and two dividers (bars), which can be arranged in $9!/(7!2!) = 36 × 35/2! = 630/2 = 315$ ways.
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