Question

Different words are being formed by arranging the letters of the word ARRANGE. All the words obtained are written in the form of a dictionary

Number of ways (words) in which neither two A's nor two R's comes together

• A. $240$
• B. $360$
• C. $660$
• D. None of these

Answer 1

Answer: (C)

$660$

Number of ways in which 2 A's are not together = $900$

Among these, let us find the cases when the 2 R's are together.

So, leaving the 2 A's, we have: RR, N, G, E i.e. 4 objects to be arranged in $4!=24$ ways.

There are 5 gaps (including the ones at the ends) for placing the 2 A's which can be done in ${}_2^{5}C=10$ ways.

Thus, total cases where A's are not together while R's are together = $24\times 10=240$

Thus, cases where A's are not together and R's are not together = $900-240=660$

Hence, (c) is correct.