Multiple choice

The number of words from the letters of the word 'BHARAT' in which B and H never come together is

  1. 360

  2. 240

  3. 120

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total arrangements of BHARAT (6 letters, 2 A's) = 6! / 2! = 360. Arrangements where B and H are together (treat BH as one unit) = 5! / 2! = 60. Since B and H can be arranged in 2 ways (BH or HB), total together = 60 * 2 = 120. Never together = 360 - 120 = 240.

AI explanation

The word BHARAT has 6 letters with A repeating twice, so the total number of arrangements is 6!/2! = 360. To find the arrangements where B and H never come together, we first treat B and H as a single unit, which creates 5 items to arrange (the BH unit, A, A, R, T) in 5!/2! = 60 ways. Since B and H can swap places within their unit, there are 60 * 2 = 120 arrangements where they are together. Subtracting this from the total gives 360 - 120 = 240.

Keep practicing — related questions