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Counting numbers with a given sum of digits

This type of question, asked 6 times: 2021 Paper 25, 25 Jun 2022, 13 Apr 2023, 9 Apr 2024, 28 Jan 2025, 29 Jan 2025. All 6 questions below, oldest first.

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  1. Question 1

    2021 Paper 25

    61
    The number of seven- digit integers with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only is

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  2. Question 2

    25 Jun 2022

    82
    The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is

  3. Question 3

    13 Apr 2023

    86
    The number of seven-digit positive integers formed using the digits 1,2,3 and 4 only and sum of the digits equal to 12 is

  4. Question 4

    9 Apr 2024

    174
    The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is

  5. Question 5

    28 Jan 2025

    146
    The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 , is____\_\_\_\_ .

  6. Question 6

    29 Jan 2025

    56
    Let PP be the set of seven -digit numbers with sum of their digits equal to 11 . If the numbers in P are formed by using the digits 1,2 and 3 only, then the number of elements in the set PP is :

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