PrepRung
Sign inSign up free

NDA 2019 Maths · Mathematics · Permutations and Combinations · medium

The number of arrangements of the letters of the word BANANA in which no two A's are adjacent is

Single correct option

The number of arrangements of the letters of the word BANANA in which no two A's are adjacent is
  1. A. 6060
  2. B. 2020
  3. C. 1212
  4. D. 3636
Show answer and solution

Answer: (C) 1212

Arrange B, N, N first: 3!2!=3\frac{3!}{2!}=3 ways. This creates 44 gaps, and the three A's go into 33 different gaps: (43)=4\binom43=4 ways. Total 3×4=123\times4=12. The value 6060 is the unrestricted count 6!3! 2!\frac{6!}{3!\,2!}.
Report a mistake

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake