How many words can be formed using the letter | vedclass

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(C) The word $BHARAT$ contains $6$ letters,where $A$ repeats $2$ times.Total number of arrangements $ = \frac{6!}{2!} = \frac{720}{2} = 360$.Now,consi

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$240$

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(C) The word $BHARAT$ contains $6$ letters,where $A$ repeats $2$ times.Total number of arrangements $ = \frac{6!}{2!} = \frac{720}{2} = 360$.Now,consider the case where $B$ and $H$ always come together. Treat $(BH)$ as a single unit. The letters are $(BH), A, R, A, T$. There are $5$ units,where $A$ repeats $2$ times.The number of arrangements where $B$ and $H$ are together $ = \frac{5!}{2!} 	imes 2! = 120 	imes 1 = 120$.Therefore,the number of words where $B$ and $H$ never come together $ = 360 - 120 = 240$.

How many words can be formed using the letters of the word $BHARAT$ such that $B$ and $H$ never come together?

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