Permutations & Combinations
Stars and Bars — Distributing Identical Objects
nta_pyq_2026_jan
Grade 11
Question:
The number of ways in which 16 oranges can be distributed to four children such that each child gets at least one orange, is
Step-by-Step Solution
Key Concept: Each child gets $\geq1$ orange. Substitute $y_i=x_i-1\geq0$: distribute 12 identical oranges among 4 children with $y_1+y_2+y_3+y_4=12$.
455 ways.
Correct Answer: 1