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Random arrangement of the letters of a word: probability of a position or order condition

This type of question, asked 2 times: 2021 Paper 11, 28 Jan 2025. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 11

    59
    Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter MM appears at the fourth position in any such word is:

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  2. Question 2

    28 Jan 2025

    131
    Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S , one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is :

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