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  • In how many ways can the letters of the word "SUCCESS" be arranged such that the vowels always come together and second letter being E?  <strong

In how many ways can the letters of the word "SUCCESS" be arranged such that the vowels always come together and second letter being E?

 

Option: 1

10


Option: 2

14


Option: 3

24


Option: 4

32


Answers (1)

To calculate the number of ways the letters of the word "SUCCESS" can be arranged such that the vowels always come together and the second letter is E, we can treat the group of vowels ("UE") as a single entity. This means we have "(UE)SSCC" to arrange.

Now, we have 4 entities to arrange, which are "(UE), S, S, C".

The 4 entities can be arranged in 4! ways. However, within this arrangement, the letter S repeats twice. Therefore, we need to divide by 2! to account for the repetition.

Additionally, within the group (UE), the vowels U and E can be arranged among themselves in 2! ways.

Therefore, the total number of arrangements where the vowels always come together and the second letter is E is given by:

(4 ! / 2 !) \times 2 !=(4 \times 3 \times 2 \times 1) /(2 \times 1) \times 2=24. Thus, there are 24 ways to arrange the letters of the word "SUCCESS" such that the vowels always come together and the second letter is E.


 

 

Posted by

Sumit Saini

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