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JEE MATHEMATICS MCQ: PERMUTATIONS

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The number of ways can 10 letters be placed in 10 marked envelopes, so that no letter is in the right envelope are
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Correct option: A
10!(1−11!+12!−13!+...+110!)10!\left( {1 - \frac{1}{{1!}} + \frac{1}{{2!}} - \frac{1}{{3!}} + ... + \frac{1}{{10!}}} \right)
Option A (10!(1−11!+12!−13!+...+110!)10!\left( {1 - \frac{1}{{1!}} + \frac{1}{{2!}} - \frac{1}{{3!}} + ... + \frac{1}{{10!}}} \right)) is correct because it represents the number of derangements of 10 objects.

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