Question

Number of words from the letters of the word BHARAT in which B and H will never come together is:

• A. 210
• B. 240
• C. 422
• D. 400

Hint:

To count permutations where certain elements should not be together, first find the total arrangements and then subtract the cases where those elements are together by treating them as a single unit.

Answer 1

The Correct Option is B

1. Total Number of Letters: - The word "BHARAT" has 6 distinct letters: B, H, A, R, A, T. 
2. Total Number of Possible Arrangements: - Since there are repeated letters (A appears twice), the total number of distinct arrangements is: \[ \frac{6!}{2!} = \frac{720}{2} = 360 \] 
3. Number of Arrangements Where B and H Are Together: - Treat B and H as a single entity. This entity along with the other letters (A, R, A, T) gives us 5 entities to arrange. 
- The number of ways to arrange these 5 entities, considering the repeated A, is: 
\[ \frac{5!}{2!} = \frac{120}{2} = 60 \] 
- Since B and H can be arranged in 2 ways (BH or HB), the total number of arrangements where B and H are together is: 
\[ 60 \times 2 = 120 \] 
4. Number of Arrangements Where B and H Are Never Together: - Subtract the number of arrangements where B and H are together from the total number of arrangements: 
\[ 360 - 120 = 240 \] Therefore, the number of words from the letters of "BHARAT" where B and H never come together is: 
\[ \boxed{240} \]