GATE CSE 2020 Q52: Derangements of LILAC with the two L's identical
- Engineering Mathematics
- 2 marks
- NAT
- No negative marking
Question
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 _______.
Try it: numerical answer: type the value
Show answer and explanation
Answer: 12 (official GATE 2020 final answer key)
Concept used: Derangement counting with a repeated letter: the L's must go to the positions not originally holding an L.
First step: L's sit at positions 1 and 3, so they must occupy two of positions 2, 4, 5; then place I, A, C in the rest avoiding their own positions.
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Source: official GATE 2020 CS question paper and final answer key, organised by IIT Delhi. Question paper · Answer key
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