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 ______.

Correct Answer:

12

**Solution:**

Given __L__ __I__ __L A C__

**Step 1:** L's are indistinguishable, by fixing their positions, we get:

- Case 1:
__L____L__ - Case 2:
__L____L__ - Case 3:
__L____L__

no character should appear in its original position

**Step 2:** Arranging the viewing letters: I, A, C

*Case 1:*__L____L__

Letter C can take only 2 places.

Letter A and I can take any of the 2 remaining places.

= 2 × 2 × 1 = 4**Case 2:**__L____L__

Letter A can take only 2 places.

Letter C and I can take any of the 2 remaining places.

= 2 × 2 × 1 = 4**Case 3:**__L____L__Letter I can take only 2 places.

Letter A and C can take any of the 2 remaining places.

= 2 × 2 × 1 = 4

Total Ways = Case 1 + Case 2 + Case 3

= 4 + 4 + 4 = 12 Ways