Permutations & Combinations
Distributing Distinct Objects — Inclusion-Exclusion
nta_pyq_2023_apr
Grade 11
Question:
The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is _____
Step-by-Step Solution
Key Concept: Inclusion-exclusion: $3^{20}-\binom{3}{1}2^{20}+\binom{3}{2}1^{20}$. (Note: PDF solution treated as identical — bonus question.)
$3^{20}-3\cdot2^{20}+3$ (bonus; answer key gives 171 for identical case).
Correct Answer: 171