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The word 'BANANA' has 6 letters: 3 A's, 2 N's, and 1 B. First, arrange the letters that are not N: B, A, A, A. The number of ways to arrange these 4 letters, with A repeated 3 times, is 4! / 3! = 4. These arrangements create 5 possible slots where the N's can be placed so that no two N's are together: _ B _ A _ A _ A _. We have 2 N's, and they are identical. So, we choose 2 of the 5 available slots to place the N's. The number of ways to do this is 5C2 = (5 × 4) / (2 × 1) = 10. The total number of arrangements where no two N's are together is the product of these two numbers: 4 × 10 = 40.