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Homework Help: How do you do this? Probability

  1. Jul 8, 2005 #1
    A computer prints out three digits chosen at random from 0 to 9 inclusive. Find the probability that:

    a) all three digits are different

    b) the third digit differs from the first two digits

    For (a) I went [tex]1/_9C_3 = 1/84[/tex]. I think it's wrong but I didn't know what else to try.

    And for (b) I don't even know where to start. :eek:
  2. jcsd
  3. Jul 8, 2005 #2


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    Homework Helper

    In both of these there are 10^3=1000 possibilities so
    probability=(# of possibilities that meat criteria)/1000
    A) try nPr since order matters.
    2) given the two numbers they are written AAB figure how many pairs of numbers are possible.
    Last edited: Jul 8, 2005
  4. Jul 9, 2005 #3
    The reason that your first answer is wrong that you havent used correctly the definition of probability : it is favourable cases/total possible cases:

    For the first one:

    Total possible numbers are 10 and not 9 , count them down if you have any confusion.
    Total number of favourable cases are [itex]10 P_3[/itex] and total possible cases are [itex]10^3[/itex].Divide them to get the answer.

    For the second one:

    Hint: You can fill first two places in anyway you want , that is 10^2 ways , and then the last one in 9 or 8 ways .Add both cases to get the required probability and divide them by / 10^3.

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