How many different words can be formed with t | vedclass

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Question

(B) The word '$BHARAT$' contains $6$ letters,where the letter '$A$' repeats $2$ times.Total number of permutations $= \frac{6!}{2!} = \frac{720}{2} =

Vedclass · Accepted Answer

$360, 240$

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(B) The word '$BHARAT$' contains $6$ letters,where the letter '$A$' repeats $2$ times.Total number of permutations $= \frac{6!}{2!} = \frac{720}{2} = 360$.To find the number of words where '$B$' and '$H$' are never together,we subtract the number of words where '$B$' and '$H$' are together from the total number of words.Treating '$BH$' as a single unit,we have $5$ units: ${BH}, A, R, A, T$. Since '$A$' repeats $2$ times,the number of arrangements where '$B$' and '$H$' are together is $\frac{5!}{2!} 	imes 2! = 120 	imes 1 = 120$.Therefore,the number of words where '$B$' and '$H$' are never together $= 360 - 120 = 240$.

How many different words can be formed with the letters of the word '$BHARAT$'? In how many of these are $B$ and $H$ never together?

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