Solution yields 120 possibilities

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what would a solution to the following problem look like?
How many "words" (distinct orderings of letters) can you make of the word BANANAS in which no As are beside each other. This may turn out to be a simple counting problem, and i apologize if i waste anyones time. My solution yields 120 possibilities i think. am i correct? thanks.
 
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I also get 120. It's easy if you first count the number of permutations of BANANAS with at least 2 As beside each other, etc.
 

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