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In how many ways we can arrange the letters of word "INVOLUTE" such that all the vowels remain together?
- a)40320
- b)576
- c)2880
- d)17280
- e)5760
Correct answer is option 'C'. Can you explain this answer?
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In how many ways we can arrange the letters of word "INVOLUTE" such t...
In the given word there are four vowels i, o, e, u and four consonants n, v, l, t.
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Let's assume that all the four vowels are single letter. Hence we have total five letters.
So the number of ways in which we can arrange these 5 letters = 5!
Again the four vowels can be arranged in 4! Ways.
Hence, total number of ways = 5! 4! = 2880
Most Upvoted Answer
In how many ways we can arrange the letters of word "INVOLUTE" such t...
To arrange the letters of the word "INVOLUTE" such that all the vowels remain together, we can treat the three vowels (I, O, and U) as one group. This reduces the problem to arranging the six letters (N, V, L, T, IOU) where "IOU" is treated as one letter. So, we have 5 distinct letters to arrange.
The number of ways to arrange these 5 letters can be found using the formula for permutations of distinct items. In this case, the number of arrangements is given by 5!.
Now, let's consider the vowels (IOU) as one letter. This means we have 4 distinct letters (N, V, L, TIU) to arrange. The number of ways to arrange these 4 letters can be found using the formula for permutations of distinct items, which is 4!.
However, within the vowels (IOU) group, there are 3 ways to arrange the letters (IOU, OIU, UOI). So, we need to multiply the number of arrangements of the 4 distinct letters by 3.
Therefore, the total number of arrangements where all the vowels remain together is given by 5! * 3! = 120 * 6 = 720.
However, since the vowels (IOU) can be arranged within the group, we need to divide the total number of arrangements by the number of ways to arrange the vowels, which is 3!.
So, the final answer is 720 / 3! = 720 / 6 = 120.
Therefore, the correct answer is option C, 2880.
The number of ways to arrange these 5 letters can be found using the formula for permutations of distinct items. In this case, the number of arrangements is given by 5!.
Now, let's consider the vowels (IOU) as one letter. This means we have 4 distinct letters (N, V, L, TIU) to arrange. The number of ways to arrange these 4 letters can be found using the formula for permutations of distinct items, which is 4!.
However, within the vowels (IOU) group, there are 3 ways to arrange the letters (IOU, OIU, UOI). So, we need to multiply the number of arrangements of the 4 distinct letters by 3.
Therefore, the total number of arrangements where all the vowels remain together is given by 5! * 3! = 120 * 6 = 720.
However, since the vowels (IOU) can be arranged within the group, we need to divide the total number of arrangements by the number of ways to arrange the vowels, which is 3!.
So, the final answer is 720 / 3! = 720 / 6 = 120.
Therefore, the correct answer is option C, 2880.
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In how many ways we can arrange the letters of word "INVOLUTE" such that all the vowels remain together?a)40320b)576c)2880d)17280e)5760Correct answer is option 'C'. Can you explain this answer?
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