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The word 'BANANA' has 6 letters: B, A, A, A, N, N. There are 3 A's, 2 N's, and 1 B.First, arrange the letters other than 'N's: B, A, A, A. The number of ways to arrange these 4 letters, with 3 A's identical, is 4! / 3! = 4 ways.These arrangements create 5 possible gaps where the 'N's can be placed to ensure no two 'N's are together: _ L1 _ L2 _ L3 _ L4 _We need to choose 2 of these 5 gaps for the two 'N's. Since the 'N's are identical, the order of placing them in the chosen gaps doesn't matter. This can be done in 5C2 ways.5C2 = (5 * 4) / (2 * 1) = 10 ways.Therefore, the total number of arrangements where no two 'N's are together is (Arrangements of BAAA) * (Ways to place N's) = 4 * 10 = 40 ways.