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.Xa.Yb.Zc.Wd
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 – 1Cr – 1, where n = 30, r = 4
∴ Number of solutions = 33C3 = 5456
Hence, option (b).
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