The number of arrangements of the letters of the word BANANA in which the two N…

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The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is

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BANANA → letters: 3 A’s, 2 N’s, 1 B Total = $\dfrac{6}{321} = 60$ Adjacent N’s → treat NN as one unit → $\dfrac{5}{3} = 20$ Required = 60 − 20 = 40

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