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  • How many ways can the letters of the word "ARRANGE" be arranged such that the two R's are always together?  Option: 1 64

How many ways can the letters of the word "ARRANGE" be arranged such that the two R's are always together?

 

Option: 1

640


Option: 2

400


Option: 3

360


Option: 4

800


Answers (1)

best_answer

To calculate the number of ways the letters of the word "ARRANGE" can be arranged such that the two R's are always together, we can treat the two R's as a single entity. Let's denote this entity as (RR).

Now, we have six entities to arrange: (RR), A, A, N, G, E.

These six entities can be arranged in 6! ways. However, within this arrangement, the two A's are repeated, so we need to divide by 2!  to account for the repetition.

Therefore, the number of arrangements where the two R's are always together is:

6 ! / 2 !=(6 \times 5 \times 4 \times 3 \times 2 \times 1) /(2 \times 1)=720 / 2=360.

Thus, there are 360 ways to arrange the letters of the word "ARRANGE" such that the two R's are always together.


 

 

 

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Gunjita

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