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  • Consider the word "ENGINEERING". In how many ways can the letters be arranged such that all the vowels always come together, but the two 'E's are not adjacent and the three 'N

Consider the word "ENGINEERING". In how many ways can the letters be arranged such that all the vowels always come together, but the two 'E's are not adjacent and the three 'N's are in alphabetical order?

 

Option: 1

9,020


Option: 2

7,600


Option: 3

8,640


Option: 4

4,680


Answers (1)

best_answer

To solve this problem, we can treat the three 'N's as distinct entities and the vowels (E, I, E, I) as a single group. We have 6 entities: (N1, N2, N3, E, I, E, I, G, R, G).

First, let's calculate the number of ways to arrange the vowels (E, I, E, I) as a single group. As there are 4 vowels, there are 4! = 24 ways to arrange them.

Next, we need to find the number of ways to arrange the remaining 6 entities: (N1, N2, N3, G, R, G). Since the three 'N's must be in alphabetical order, we can consider them as separate entities within this group. So, we have 6 entities to arrange: (N1, N2, N3, G, R, G).

Considering the two 'G's as distinct, we have 6 ! / 2 !=360 ways to arrange these 6 entities.
Finally, we multiply the number of ways to arrange the vowels and the remaining entities:
24 \times 360=8640

Therefore, the total number of ways to arrange the letters of the word "ENGINEERING" such that all the vowels always come together, but the two 'E's are not adjacent and the three 'N's are in alphabetical order, is 8640.

 

Posted by

Kuldeep Maurya

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