Question

How many words can be made from the letters of the word BHARAT in which B and H never come together.

• A. $360$
• B. $300$
• C. $240$
• D. $120$

Answer 1

The correct option is B $300$

there are $6$ letters in which $2$ are same

therefore the number of words are there are $6$ letters in which $2$ are same

therefore the total number of words that can be formed are $\frac{6!}{2!}=360$

the number of words where B and H never come together are total word - number of words where B and H come together

number of words where B and H come together are calculated by considering B and H as $1$ letter

therefore the number of words are $\frac{5!}{2!}=60$

therefore the number of words where b and h do not come together are $360-60=300$