Permutations and Combinations
Inclusion-Exclusion Principle
IIT-JEE 2012 Paper 1
Grade 11
Question:
The total number of ways in which $5$ balls of different colours can be distributed among $3$ persons so that each person gets at least one ball is:
(1) $75$
(2) $150$
(3) $210$
(4) $243$
Step-by-Step Solution
Key Concept: Inclusion-exclusion (surjections): $3^5 - \binom{3}{1}2^5 + \binom{3}{2}1^5 = 243 - 96 + 3 = 150$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)