📐 Mathematics · Permutations and Combinations · JEE

Number of non-negative integer solutions to x₁ + x₂ + x₃ = 10:

Answer: 66.

Correct answer: A. 66

Explanation: Stars and bars with n=10, r=3 groups. Solutions = C(10+3−1, 3−1) = C(12,2) = 12×11/2 = 66.

Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.

Concept context

Counting, arrangements, and selections