Q.The number of solutions of the equation $x_1 + x_2 + \cdots + x_8 = 20$ where each $x_i$ is a non-negative integer not exceeding 4 is equal to the coefficient of $x^{20}$ in

(1 + x + x^2 + x^3 + x^4)^8

(1 - x^5)^8 (1 - x)^{-8}

(1 + x + \cdots + x^4)^8

directly

both (a) and (b)

The correct solution involves applying the fundamental concept to derive the final value step by step...

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Q.The number of solutions of the equation x1+x2+⋯+x8=20x_1 + x_2 + \cdots + x_8 = 20x1​+x2​+⋯+x8​=20 where each xix_ixi​ is a non-negative integer not exceeding 4 is equal to the coefficient of x20x^{20}x20 in