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  • In how many ways can the letters of the word "SUCCESS" be arranged such that the vowels always come together?  Option: 1 464

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

 

Option: 1

4640


Option: 2

2400


Option: 3

6400


Option: 4

3720


Answers (1)

best_answer

To calculate the number of ways the letters of the word "SUCCESS" can be arranged such that the vowels always come together, we can treat the group of vowels ("UE") as a single entity. This way, we have "SCCSS(UE)" to arrange.

Now, we have 6 entities to arrange, which are "S, C, C, S, S, (UE)".

The 6 entities can be arranged in 6! ways. However, within this arrangement, the letter S repeats three times. Therefore, we need to divide by 3! 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 is given by:

\mathrm{(6 ! / 3 !) \times 2 !=(6 \times 5 \times 4 \times 3 \times 2 \times 1) /(3 \times 2 \times 1) \times 2=2,400}.

Thus, there are 2,400 ways to arrange the letters of the word "SUCCESS" such that the vowels always come together.

 

Posted by

Rakesh

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