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
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Crostul, Siong Thye Goh, N. F. Taussig, Thomas Andrews, Namaste
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 $6! - (2)(5!)$.