Question

Find the number of arrangements of the letters of the word ‘BANANA’ in which the two N’s do not appear adjacently.

Answer 1

Considering the two N’s as one letter, the number of letters to be arranged = 5. 

Therefore, the number of arrangements = \(\frac{5!}{3!}=20\)   (∵ A repeated 3 times) 

Total number of arrangements if there were no restriction imposed = \(\frac{6!}{3!2!} = 60.\)          

(A repeated 3 times and N repeated 2 times) 

∴ Required number of arrangements = 60 – 20 = 40.