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How many ways can the letters of the word ANALYTICAL be arranged so that the two L's are never next to each other?
- 8!
- 6 * 8!
- (8! / 3!)⁴
- 9!
Correct answer: 6 * 8!
Solution
ANALYTICAL has 10 letters: A(3), N(1), L(2), Y, T, I, C. Total distinct arrangements = 10!/(3!*2!) = 302400. When both L's are together treat LL as one unit giving 9 letters with A(3) repeated: 9!/3! = 60480. Non-adjacent = 302400 - 60480 = 241920 = 6 * 8!.
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