Answer: (n+1)(n+2)/2.
- A n+1, the count for a two-variable expansion
- B n+2, one more than the two-variable case
- C (n+1)(n+2)/2
- D 3n, treating each variable as contributing separately
Correct answer: C. (n+1)(n+2)/2
Explanation: Number of terms in expansion of (a+b+c)<sup>n</sup> = (n+1)(n+2)/2 (using stars and bars).
Row n of Pascal's triangle gives the coefficients nC0, nC1, ..., nCn for the expansion of (a+b)ⁿ; each number is the sum of the two numbers diagonally above it, a direct visual proof of the identity nCr = (n-1)C(r-1) + (n-1)Cr.
Concept context
Expansion of (a+b) n , general term, middle term, binomial coefficients, and greatest term