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The word BANANA has 6 letters: B, A, N, A, N, A. There are 3 A's and 2 N's.To ensure no two N's are together, first arrange the other letters: B, A, A, A.The number of ways to arrange B, A, A, A is 4! / 3! = 4.Now, place the 2 N's in the spaces created by these letters: _ B _ A _ A _ A _.There are 5 possible spaces. We need to choose 2 of these spaces for the two N's. This can be done in 5C2 ways = (5 * 4) / (2 * 1) = 10 ways.Therefore, the total number of arrangements where no two N's are together is 4 (arrangements of BAAA) * 10 (placing N's) = 40.