Find the greatest coefficient in the expansion of `(a + b + c+ d)^(15)`.

Explanation

To find the greatest coefficient in the expansion of \((a + b + c + d)^{15}\), we can use the multinomial theorem. The multinomial expansion states that:

\[ (x_1 + x_2 + \ldots + x_k)^n = \sum_{i_1 + i_2 + \ldots + i_k = n} \frac{n!}{i_1! i_2! \ldots i_k!} x_1^{i_1} x_2^{i_2} \ldots x_k^{i_k} \]

where \(i_1, i_2, \ldots, i_k\) are non-negative integers.

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