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  • In how many ways can the letters of the word "SUCCESS" be arranged such that the vowels never come together?Option: 1 1800<di

In how many ways can the letters of the word "SUCCESS" be arranged such that the vowels never come together?

Option: 1

1800


Option: 2

2600


Option: 3

5400


Option: 4

4720


Answers (1)

best_answer

To calculate the number of ways the letters of the word "SUCCESS" can be arranged such that the vowels never come together, we need to consider the arrangement of consonants and vowels separately.

First, let's arrange the consonants "S, C, C, S, S":

The number of ways to arrange the consonants without any restrictions is given by 5! as there are 5 distinct consonants to arrange.

Next, let's consider the placement of the vowels "U" and "E" among the consonants. We can think of them as separators between the consonants to ensure they never come together. We have 6 possible positions where we can place the vowels:

_ C _ C _ S _ S _

Since there are 6 positions and we need to select 2 of them to place the vowels, the number of ways to arrange the vowels is given by C(6, 2):

\mathrm{C(6,2)=6 ! /(2 ! \times(6-2) !)=6 ! /(2 ! \times 4 !)=(6 \times 5) /(2 \times 1)=15 }.

Therefore, the total number of ways to arrange the letters of the word "SUCCESS" such that the vowels never come together is given by the product of the arrangements of the consonants and vowels:

\mathrm{5 ! \times C(6,2)=5 ! \times 15=120 \times 15=1800 }.

Thus, there are 1800 ways to arrange the letters of the word "SUCCESS" such that the vowels never come together.

 

Posted by

Anam Khan

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