A person goes in for an examination in which there are four papers with a maximum of \( m \) marks from each paper. The number of ways in which one can get 2 m marks is
\( \text{The required number} = \text{Coeff of } x^{2m} \text{ in } (1 - x^m + 1)^4 (1 - x)^{-4} \)
\( = \text{Coeff of } x^{2m} \text{ in } (x^0 + x^1 + \dots + x^m)^4 \)
\( = \frac{(2m + 1)(2m + 2)(2m + 3)}{6} - \frac{4m(m + 1)(m + 2)}{6} \)
\( = \frac{(m + 1)(2m^2 + 4m + 3)}{3} \)
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