Permutations & Combinations
Stars and Bars — Distribution with Minimum Constraint
nta_pyq_2024_jan
Grade 11
Question:
The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is
Step-by-Step Solution
Key Concept: Give each child 2 apples first (6 total used), leaving 15 to freely distribute among 3 children. Apply stars and bars: $\binom{15+2}{2}=\binom{17}{2}$.
15 apples among 3 children freely: ${}^{17}C_2=136$.
Correct Answer: 4