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Words from all letters of a word with some letters together or never together

This type of question, asked 4 times: 2021 Paper 22, 1 Feb 2023, 8 Apr 2023, 23 Jan 2025. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 22

    87
    The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is

  2. Question 2

    1 Feb 2023

    82
    The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is

  3. Question 3

    8 Apr 2023

    156
    If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which CC and SS do not come together, is (6!) kk, then kk is equal to

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  4. Question 4

    8 Apr 2023

    69
    The number of arrangements of the letter of the word "INDEPENDENCE" in which all the vowels always occur together is

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  5. Question 5

    23 Jan 2025

    62
    The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is

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