PROBAbility!!!!

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A bag contains 150 balls numbered 1 through 150. Three balls are drawn and placed on the table. The probability that the balls were drawn in increasing order can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?

  • PROBAbility!!!! -

    number of ways to draw 3 balls from 150
    = 150x149x148 = 3307800

    But these include triplets of the form
    ABC
    ACB
    BAC
    BCA
    CAB
    CBA , that is , containing the same three numbers.
    Only one of these 6 would have them in the correct increasing order ,so we divide 3307800 by 6 to get 551300
    so the prob of your event = 551300/3307800
    = 1/6

    so a/b = 1/6, and a+b = 7

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