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Selecting a committee or team from groups with at least / at most conditions

This type of question, asked 7 times: 2021 Paper 1, 26 Jun 2022, 24 Jan 2023, 25 Jan 2023, 30 Jan 2024, 7 Apr 2025, 5 Apr 2026 S2. All 7 questions below, oldest first.

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  1. Question 1

    2021 Paper 1

    62
    A scientific committee is to formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is:

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  2. Question 2

    26 Jun 2022

    82
    There are ten boys B1,B2,….,B10B_{1},B_{2},\ldots.,B_{10} and five girls G1G_{1}, G2,….,G5G_{2},\ldots.,G_{5} in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1B_{1} and B2B_{2} together should not be the members of a group, is

  3. Question 3

    24 Jan 2023

    87
    A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is

  4. Question 4

    25 Jan 2023

    178
    Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer 5 fruits to Anil is

  5. Question 5

    30 Jan 2024

    176
    In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A, B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is

  6. Question 6

    7 Apr 2025

    57
    From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is.

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  7. Question 7

    5 Apr 2026 S2

    59
    A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is:

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