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

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

Filo · Accepted Answer

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.

Question Text	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
Answer Type	Text solution:1
Upvotes	151

Text solutionVerified