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?

Wed September 12, 2012

In the word ARRANGE, there are:

2 AÂ’s, 2 RÂ’s, 1 N, 1 G and 1 E

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

Consider 2 AÂ’s as a single letter and two RÂ’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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