Question

The number of terms which are not similar in the expansion of $(l + m + n)^6$ is

• A. 7
• B. 42
• C. 28
• D. 21

Answer 1

Answer: (C)

28

Answer 2

The number of terms in the expansion of $(x_1 + x_2 + \dots + x_k)^n$ is given by the stars and bars formula $\binom{n+k-1}{k-1}$. In this case, $n=6$ and $k=3$ (for $l, m, n$). So the number of terms is $\binom{6+3-1}{3-1} = \binom{8}{2} = \frac{8 \times 7}{2} = 28$.