MathematicsThe number of ways in which the letters of the word ARRANGE be arranged so that “two A’s are together but not two R’s”

The number of ways in which the letters of the word ARRANGE be arranged so that “two A’s are together but not two R’s”

The number of words in which both A’s are together

is $\frac{6!}{2!} = 360$

the no. of words in which both A’s and both R’s are together is $5! = 120$

therefore the no. of words in which both A’s are together but the tow R’s are not together is $360 - 120 = 240$

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