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Arrangements with some letters or people restricted to particular places

This type of question, asked 4 times: 2 May 2023 S2, 12 May 2024 S2, 11 Apr 2026 S1, 17 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    137
    Number of different nine-digit numbers that can be formed from the digits in 223355888 by rearranging, so that the odd digits occupy even positions, is

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  2. Question 2

    12 May 2024 S2

    119
    The number of words that can be formed by using the letters of the word CALCULATE such that each word starts and ends with a consonant, are

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  3. Question 3

    11 Apr 2026 S1

    53
    There are 55 boys and 33 girls seated in a row for a photograph. The number of ways in which a photograph can be taken if the girls occupy only odd places is...

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  4. Question 4

    17 Apr 2026 S1

    52
    The number of arrangements of the letters in the word SOLAPUR, so that consonants and vowels are placed alternately is

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