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Question
Select the correct answer from the given alternatives.
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently
Options
80
60
40
100
Solution
40
Explanation;
Arrange B, A, A, A in `(4!)/(3!)` ways.
These four letters create 5 gaps in which 2N are to be filled, this can be done in 5C2 ways, we do not permute those 2N as they are identical.
Required number = `(4!)/(3!) xx ""^5"C"_2` = 40
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