Find the coffiecient of `x^2 y^3 z^4 ` w in the expansion of `(x-y-z+w)^(10)`

Explanation

To find the coefficient of \(x^2 y^3 z^4 w\) in the expansion of \((x - y - z + w)^{10}\), we can use the multinomial theorem. The multinomial theorem states that for any positive integer \(n\) and any non-negative integers \(p, m, q, r\) such that \(p + m + q + r = n\):

\[ (a_1 + a_2 + a_3 + a_4)^n = \sum \frac{n!}{p! m! q! r!} a_1^p a_2^m a_3^q a_4^r \]

In our case, we want to find the coefficient of \(x^2 y^3 z^4 w\) in the expansion of \((x - y - z + w)^{10}\). Here, we can identify:

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