In how many ways can the letter of the word PERMUTATIONS can be ar | Filo
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Class 11

Math

Algebra

Permutations and Combinations

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In how many ways can the letter of the word can be arranged so that all the vowels come together

  1. 2419200
Correct Answer: Option(a)
Solution: There are total letters in the word , with repeated twice.
Number of vowels in the given word are .
Since vowels have to always occur together, so they are considered as a single object . This single object (letter) together with the remaining letters will give us objects (letters).  
These objects in which there are can be arranged in ways .Corresponding to each of these arrangements, the different vowels can be arranged in ways.
Therefore, by multiplication principle, required number of arrangements in this case

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