Permutations & Combinations
Distributing Distinct Objects into Identical Groups — Stirling Numbers
nta_pyq_2024_jan
Grade 11
Question:
If $n$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $n$ is equal to:
Step-by-Step Solution
Key Concept: Count the number of ways to partition 5 distinct people into at most 4 non-empty indistinguishable groups. Enumerate all partition types of 5 into $\leq4$ parts.
Counting all partition types: $1+5+10+15+10+10=51$.
Correct Answer: 3