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  • How many ways can the letters of the word "ARRANGE" be arranged such that the two R's are never together and first letter being N?  

How many ways can the letters of the word "ARRANGE" be arranged such that the two R's are never together and first letter being N?

 

Option: 1

20


Option: 2

32


Option: 3

24


Option: 4

30


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 never together and the first letter is N, we can consider the placement of the R's and N separately.

Let's consider the placement of the two R's first. We have 6 entities to arrange: N, A, G, E, and two R's (R1 and R2). Since we want to ensure that the two R's are never together, we can think of placing the R's in alternate positions, creating a pattern like R_A_R_A.

There are three possible positions for the first R, and once it's placed, there are two possible positions for the second R.

Next, let's consider the placement of the first letter N. We have already placed the two R's, so there are four remaining positions for the N: N _ _ _ _.

Therefore, the number of ways to arrange the letters of "ARRANGE" such that the two R's are never together and the first letter is N is given by:

3 (positions for the first R) \times2 (positions for the second R) \times 4 (positions for the first letter N) = 24.

Thus, there are 24 ways to arrange the letters of the word "ARRANGE" such that the two R's are never together, and the first letter is N.

 

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Gunjita

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