Answer: (1+x)n = sum nCr × xr.
- A (1+x)n = sum nCr × xr
- B xn, the generating function associated with a single term
- C n! x, a linear function mistaken for a generating series
- D ex, the exponential generating function for permutations, not combinations
Correct answer: A. (1+x)n = sum nCr × xr
Explanation: Binomial theorem: (1+x)ⁿ = Σᵣ₌₀ⁿ C(n,r)xʳ. The coefficient of xʳ is exactly C(n,r). This is the ordinary generating function for the sequence of binomial coefficients.
Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.
Concept context
Counting, arrangements, and selections