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  • In how many ways can the letters of the word "ENGINEER" be arranged such that the N and E should not be together?  Option: 1 <p

In how many ways can the letters of the word "ENGINEER" be arranged such that the N and E should not be together?

 

Option: 1

2,127,253


Option: 2

9,916,656


Option: 3

2,902,040


Option: 4

8,258,963


Answers (1)

best_answer

To calculate the number of ways the letters of the word "ENGINEER" can be arranged such that the letters N and E are not together, we can treat the N and E as distinct entities and count the number of valid arrangements.

The word "ENGINEER" has a total of 8 letters, but since the N and E are treated as distinct entities, we have a total of 8 + 2 = 10 objects to arrange.

We can arrange these 10 objects in 10! ways. However, within this arrangement, we have to account for the cases where the N and E are together.

Consider the NE as a single entity. We can arrange these 9 entities ("NE, G, I, N, E, E, R") in 9! ways. Within each of these arrangements, the N and E can be rearranged among themselves in 2! ways.

Therefore, the total number of arrangements where the N and E are not together is given by:

10 !-(9 ! \times 2 !)=3,628,800-(362,880 \times 2)=3,628,800-725,760=2,902,040

Thus, there are 2,902,040 ways to arrange the letters of the word "ENGINEER" such that the letters N and E are not together.

 

Posted by

Shailly goel

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