MATH

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A committee of 5 people is to be selected from student council. Council has 6 boys and 7 girls. What is the probability that the committee will have at least 3 boys?

*** If you can show work that would be helpful (OPTIONAL)***

THANK YOU VERY MUCH!

  • MATH -

    Define
    C(n,r)=n!/(r!(n-r)!)=n choose r
    Sample space: C(13,5)=1287

    ways to choose 0 boy
    =Choose 5 girls out of 7 and 0 boy out of 6
    =C(7,5)*C(6,0)=21

    ways to choose 1 boy:
    =C(7,4)*C(6,1)=210

    ways to choose 2 boys:
    =C(7,3)*C(6,2)=525

    ways to choose 3 boys:
    =C(7,2)*C(6,3)=420

    ways to choose 4 boys:
    =C(7,1)*C(6,4)=105

    ways to choose 5 boys:
    =C(7,0)*C(6,5)=6

    If you add them all up, they will total 1287 as required.

    Now make appropriate sums according to requirements and calculate probability.

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