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Number of integer solutions of x + y + z + ... = n with lower or upper bounds (identical objects to persons)

This type of question, asked 6 times: 28 Jun 2022, 1 Feb 2023, 11 Apr 2023, 31 Jan 2024, 5 Apr 2024, 23 Jan 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    28 Jun 2022

    153
    The number of ways to distribute 30 identical candies among four children C1,C2,C3C_{1},C_{2},C_{3} and C4C_{4} so that C2C_{2} receives atleast 4 and atmost 7 candies, C3C_{3} receives atleast 2 and atmost 6 candies, is equal to

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  2. Question 2

    1 Feb 2023

    178
    Number of integral solutions to the equation x+y+z=21x + y + z = 21, where x≥1,y≥3,z≥4x \geq 1,y \geq 3,z \geq 4, is equal to

  3. Question 3

    11 Apr 2023

    66
    The number of triplets (x,y,z)(x,y,z). where x,y,zx,y,z are distinct non negative integers satisfying x+y+z=15x + y + z = 15, is

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  4. Question 4

    31 Jan 2024

    151
    The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

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  5. Question 5

    5 Apr 2024

    84
    The number of ways of getting a sum 16 on throwing a dice four times is

  6. Question 6

    23 Jan 2026 S2

    65
    The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

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