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Counting numbers divisible by a given number formed from given digits

This type of question, asked 3 times: 16 May 2023 S2, 22 Apr 2025 S2, 12 May 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    16 May 2023 S2

    148
    A five-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4, 5 without repetition, then the total number of ways this can be done is

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  2. Question 2

    22 Apr 2025 S2

    141
    If four digit numbers are formed by using the digits 1,2,3,4,5,6,71,2,3,4,5,6,7 without repetition, then out of these numbers, the numbers exactly divisible by 25 are

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  3. Question 3

    12 May 2026 S2

    57
    How many different five digit numbers which are divisible by 44 can be formed using the digits in the number 2245722457 ?

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