GATE | GATE CS 2020 | 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 ________ .

Note – This question was Numerical Type.
(A) 12
(B) 10
(C) 8
(D) 15


Answer: (A)

Explanation: There are 3 choices for the first slot, and then 2 for the third slot. That leaves one letter out of I,A,C unchosen and there are 2 slots that one might occupy. After that, the L′s must go in the 2 unfilled slots.

Hence the answer is,

3×2×1×2 = 12 

Option (A) is correct.

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