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

Answer 1

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