Question

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

A
40
B
60
C
80
D
100

Solution

## The correct option is A $$40$$We can arrange $$B,A,A,A$$ in $$\displaystyle \frac { 4! }{ 3! } =4$$ waysFor 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 $$=4(10)=40$$Maths

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