GATE 2020 CS – Question 52
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L's are indistinguishable, is ______.
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Correct answer: 12 to 12
Explanation
Treat the L's as distinct: derangements of 5 items = 44. Then the count with L's indistinguishable follows by inclusion-exclusion over the L positions: swapping the two L's gives the same word in both cases only once, so the count is 44/2 - (adjustments) = 12 by direct enumeration. Answer: 12.