Permutations and Combinations
Inclusion-Exclusion Principle
JEE Advanced 2020 Paper 2
Grade 11
Question:
In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms such that each room contains at least one person. The number of ways is _____.
Step-by-Step Solution
Key Concept: Count surjections from 6 persons onto 4 distinct rooms via inclusion-exclusion: $4^6 - \binom{4}{1}3^6 + \binom{4}{2}2^6 - \binom{4}{3}1^6 = 4096 - 2916 + 384 - 4 = 1560$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 1560