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3 January, 12:11

The math club at a certain school has 10 members, of which 6 are seniors and 4 juniors. In how many ways can they form a group of 5 members to go to a tournament, if at least 4 of them have to be seniors (aka either a group of 4 seniors and 1 junior, or a group of 5 seniors

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  1. 3 January, 13:10
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    Answer: 66 ways

    Step-by-step explanation:

    Given;

    Number of senior math club members = 6

    Number of junior math club members = 4

    Total number of members of the club = 10

    To form a group of 5 members with at least 4 seniors.

    N = Na + Nb

    Na = number of possible ways of selecting 4 seniors and 1 junior

    Nb = number of possible ways of selecting 5 seniors.

    Since the selection is does not involve ranks (order is not important)

    Na = 6C4 * 4C1 = 6!/4!2! * 4!/3!1! = 15 * 4 = 60

    Nb = 6C5 = 6!/5!1! = 6

    N = Na + Nb = 60+6

    N = 66 ways
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