Question
Tue September 11, 2012 By:
 

In how many ways can the letters of the word 'ARRANGE ' be arranged so that neither the two A 's nor the two R 's are together?

Expert Reply
Wed September 12, 2012

 

In the word ARRANGE, there are:

2 A’s, 2 R’s, 1 N, 1 G and 1 E

So, the letters of the word ARRANGE can be arranged in 7!/(2! × 2!) = 1260 ways.

 

Consider 2 A’s as a single letter and two R’s as also a single letter. Now these two letters (single letter by combining 2As + single letter by combining 2 Rs) and the remaining 3 letters can be arranged in 5! = 120 ways.

 

Therefore, the number ways in which the letters of the word 'ARRANGE ' be arranged so that neither the two A 's nor the two R 's are together = 1260 - 120 = 1140.

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