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?
Asked by | 11th Sep, 2012, 06:22: PM
In the word ARRANGE, there are:
2 As, 2 Rs, 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 As as a single letter and two Rs 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.
Answered by | 12th Sep, 2012, 11:27: AM
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Verify mobile number
Enter the OTP sent to your number