In how many ways the letters of the word 'EXCELLENT' can be arranged so that the vowels are always together?

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QuestionIn how many ways the letters of the word 'EXCELLENT' can be arranged so that the vowels are always together?

Solution,

Total no. of letters in given word= 9

Number of L’s = 2 times

Number of E’s = 3 time

According to the question,

The vowel letter (3E) must come together then 3E is considered as 1 letter

Then, remaining total letter (n)= 6+1

Thus, The total arrangement in which 3E always comes together =$\frac{7!}{2}$ =2520 Ways

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