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Maths

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Eleven people, 7 men and 4 women, successfully completed their study at the School of Astronautics. A team of 6 people needs to be selected from them for the next intergalactic travel. In how many ways can 6 astronauts be selected, if at least 2 women and 3 men must be in the team?

thank u!!

  • Maths - ,

    For at least 2 women and 3 men, the only cases would be
    2W,4M = C(4,2) x C(7,4) = 6x35 = 210 , or
    3W,3M = C(4,3) x C(7,3) = 4x35 = 140

    for a total of 350 ways

    (all possible ways would be
    0W,6M
    1W,5M
    2W,4M
    3W,3M
    4W 2M )

  • Maths - ,

    Worked out combination of women and men
    Either 3 women and 3 men or 4 men and 2 women
    Then comination for the 2 Women was n = 4 no. of combos was 6 and r = 2 and for the 3 women n = 4 and r = 3 no. of combos was 4

    Follow the formula n!/(n-r)! x (r!)

    Same process for men. In each instance 35 combinations for Men.

    Then times combination for each set which was (6 x 35) + (4 x 35) = 350

    350 combinations for the team

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