Class 11

Math

Algebra

Permutations and Combinations

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

- $40$
- $60$
- $80$
- $100$

Now taking two of the N's together,

NN B A A A ...... by taking NN as one block

we get

$3!5! $ due to repetitions of $3A_{′}$s.

$3!5! $ due to repetitions of $3A_{′}$s.

Hence, the required permutation will be

$3!2!6! −3!5! $

$=60−20$

$=40$