Multiple choice

The number of words from the letters of the word $'BHARAT'$ in which B and H will 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. Arrangements of (BH), A, R, A, T = 5! / 2! = 60. Since BH can be HB, multiply by 2 = 120. Total - Together = 360 - 120 = 240.

AI explanation

The word BHARAT has 6 letters where A is repeated twice, so the total number of arrangements is 6 factorial divided by 2 factorial, which equals 360. To find the arrangements where B and H are never together, treat B and H as a single block, giving 5 units to arrange, which is 5 factorial divided by 2 factorial, equaling 60. These blocks can be arranged in two ways internally as BH or HB, giving 120 arrangements where they are together. Subtracting this from the total gives 360 minus 120, which is 240.

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