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Question

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


A
40
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B
60
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C
80
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D
100
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Solution

The correct option is A $$40$$
We can arrange $$B,A,A,A$$ in $$\displaystyle \frac { 4! }{ 3! } =4$$ ways
For each arrangement of these four letters, there are five places (marked with $$X$$) for $$N$$ as shown below
$$X - X - X - X - X$$
We can choose two out of these five in $$^{ 5 }{ { C }_{ 2 } }=10$$ ways.
Thus the required number of ways $$=4(10)=40$$

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