The letters of the word LOVERS must be used to form a different word arrangement without repeating the letters. How many word arrangements are possible if the letters L and O can not be side by side?


closed as off-topic by Crostul, Siong Thye Goh, N. F. Taussig, Thomas Andrews, Namaste Aug 31 '17 at 22:57

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  • $\begingroup$ 4*5!........... $\endgroup$ – Jasser Aug 31 '17 at 7:27
  • 1
    $\begingroup$ Welcome to MathSE. When you pose a question here, it is expected that you include your own thoughts on the problem. For an exercise such as this, you should include your attempt and indicate where you are stuck so that you receive responses appropriate to your skill level. $\endgroup$ – N. F. Taussig Aug 31 '17 at 9:33

First of all, on this forum, you should have shown in your question that you at least attempted the problem. Bear in mind next time.

'# of arrangements with 6 letters (all possible permutations without restrictions): $6!$

'# of arrangements with "l" "o" sticking together as "lo": $5!$

'# ... as "ol": $5!$

Thus the answer is $6! - (2)(5!)$.


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