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In how many different ways can the letters of the word  “LEADING”  be arranged in such a way that the vowels always come together?

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Permutations & Combinations Admin 3 years 6 Answers 1022 views 0

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    Ans is 5! x 3!

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    total vowels 3,always come togather ,so AEI L D N G , here all 5 can arrange in fact 5 ways , and three vowel can arrange in fact 3 ways , so final is fact 3* fact 5 .

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    I think it is 720.
    group all vowels as one and do it. you will get.

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    leading = 4 con and 3 vow. ldng(eai) = 4!/1! * 3!/1! = 144

  5. Admin

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    ‘LEADING’ has 7 different letters.
    Vowels EAI are always together, So it is one letter.
    Then, we have to arrange the letters LNDG (EAI).
    Now, 5 (4 + 1) letters can be arranged in 5! = 120 ways.
    The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
    Required number of ways = (120 x 6) = 720

  6. Dhruv Patel

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    24 ways are there.

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