What is the number of distinct terms in the expansion of (a + b + c)^20

What is the number of distinct terms in the expansion of (a + b + c)20?

  1. 210
  2. 231
  3. 242
  4. 253

Answer

Number of terms in the given expansion is nothing but the non-negative integral solutions of the equation:

a + b + c = 20

Total number of non-negative integral solutions

(20+3-1)C(3-1) = 22C2 = 231

The correct option is B.