How many words can be formed using the letter | vedclass

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Question

(B) The word $BHARAT$ contains $6$ letters,where the letter $A$ is repeated twice.Total number of arrangements $= \frac{6!}{2!} = \frac{720}{2} = 360$

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(B) The word $BHARAT$ contains $6$ letters,where the letter $A$ is repeated twice.Total number of arrangements $= \frac{6!}{2!} = \frac{720}{2} = 360$.To find the number of words where $B$ and $H$ are together,we treat $(BH)$ as a single unit.Now,we have $5$ units: $(BH), A, R, A, T$.The number of arrangements of these $5$ units,where $A$ is repeated twice,is $\frac{5!}{2!} = \frac{120}{2} = 60$.Since $B$ and $H$ can be arranged among themselves in $2! = 2$ ways,the total number of arrangements where $B$ and $H$ are together is $60 	imes 2 = 120$.Therefore,the number of words where $B$ and $H$ are never together $= 	ext{Total arrangements} - 	ext{Arrangements where } B 	ext{ and } H 	ext{ are together}$.$= 360 - 120 = 240$.

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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