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  • How many ways can the letters of the word "ARRANGE" be arranged such that the two A's are always together?  Option: 1 40

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

 

Option: 1

40


Option: 2

30


Option: 3

20


Option: 4

10


Answers (1)

best_answer

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

Now, we have five entities to arrange: (AA), R, R, N, G, E.

These five entities can be arranged in 5! ways. However, within this arrangement, the two R's repeat, so we need to divide by 2! to account for the repetition.

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

5 ! / 2 !=(5 \times 4 \times 3 \times 2 \times 1) /(2 \times 1)=60 / 2=30.

Thus, there are 30 ways to arrange the letters of the word "ARRANGE" such that the two A's are always together.
 

 

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Rishabh

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