LILAC = positions 1..5 originally L,I,L,A,C, with the two L's indistinguishable (so there are 5!/2! = 60 distinct arrangements of the multiset {L,L,I,A,C} total). We need arrangements where position 1≠L, position 2≠I, position 3≠L, position 4≠A, position 5≠C. Applying inclusion-exclusion over these 5 'bad' events across the 60 multiset arrangements (carefully accounting for the repeated L when both L-positions are simultaneously forced or freed) yields exactly 12 valid arrangements — this is the well-documented official GATE 2020 answer for this specific multiset-derangement count.