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Question #41116
The Question
Let be a multiset containing 12 elements, consisting of 6 identical items of type and 6 distinct items . Find the number of ways to partition the multiset into 6 unordered pairs.
Options
- A.
76
- B.
151
- C.
196
- D.
256
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Monster
Ultra-high difficulty questions designed to test your limit, stamina, and deep conceptual understanding.
Concepts Behind This Question
Equivalence Class Partitioning|Division into Groups|Selection from Identical Items
Why This Question Is Tricky
Common Mistakes
This problem targets the 'Selection from Identical Items' trap within equivalence class partitioning.
Students frequently attempt to use the standard multinomial coefficient formula for division into groups, failing to recognize that it only applies to distinct items.
When a multiset contains identical items, the indistinguishability of the items fundamentally alters the symmetry of the partitions, requiring systematic case analysis based on the distribution of the identical elements.
A secondary lethal trap occurs within the cases: students often forget to divide by the symmetry factor (e.g., ) when forming unlabelled groups of the remaining distinct items, leading to significant overcounting (such as arriving at 196 instead of 76).
Quick Facts About This Question
Question Information
| Subject | Mathematics |
| Chapter | Relations and Functions - Class 12 |
| Concept | Equivalence Class Partitioning |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |