Permutations & Combinations
Partitions of Identical Objects into Identical Containers
nta_pyq_2024_jan
Grade 11
Question:
Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
Step-by-Step Solution
Key Concept: Count integer partitions of 8 into at most 4 parts (books and shelves both identical). Enumerate by number of empty shelves.
Integer partitions of 8 into $\leq4$ parts: $1+4+5+5=15$.
Correct Answer: 4