Derangements
The number of ways in which 4 letters can be placed in 4 addressed envelopes such that no letter goes to the correct envelope is
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About This Question
- Subject
- mathematics
- Chapter
- permutations and combinations
- Topic
- derangements
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
9
- Problem Identification: This is a direct application of the 'Derangement' formula, Dn.
- Formula: Dn=n!(1−1!1+2!1−3!1+⋯+n!(−1)n).
- Substitute n=4:
- D4=4!(1−1+21−61+241)
- Calculation:
- D4=24(2412−4+1)
- D4=12−4+1=9.
- Result: 9 ways.
This hard difficulty mathematics question is from the chapter permutations and combinations, covering the topic of derangements. It appeared in the 2025 exam.
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