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Question:

The number of distinct terms in the expansion of (X + Y + Z + W)³⁰ are:

Explanation:

All the terms in the expansion of (X + Y + Z + W)³⁰ are of the form k.X^a.Y^b.Z^c.W^d

Where a + b + c + d = 30

∴ The number of terms in the expansion is equal to the number of non-negative integer solutions of the equation a + b + c + d = 30

The number of solutions of this equation is given by

ⁿ + r – 1C_r – 1, where n = 30, r = 4

∴ Number of solutions = ³³C₃ = 5456

Hence, option (b).