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    You have eight numbered balls ~ 1,2,3,4,5,6,7,8

    You choose three numbered balls which appeal to you. Say 1,2,3.

    Then you put the eight numbered balls in a bag and pick out three balls.

    What is the probability of you then pulling out 1,2 and 3?
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    (Original post by Fonda1971)
    You have eight numbered balls ~ 1,2,3,4,5,6,7,8

    You choose three numbered balls which appeal to you. Say 1,2,3.

    Then you put the eight numbered balls in a bag and pick out three balls.

    What is the probability of you then pulling out 1,2 and 3?
    Do you mean 1, 2, 3 in that order or 1, 2, 3, in any order? Please post what you've tried so far and say exactly where you're stuck.
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    Hi, thanks for helping.

    1,2,3 in any order.

    I’ve no clue how to work this question out and would appreciate any help!
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    Q1) How many ways are there of choosing 3 balls from 1, 2, 3, ..., 8?
    Q2) How many ways are there of choosing 1, 2, 3 from 1, 2, 3, ... 8?

    Note: "choosing" has a technical meaning here - it means "order doesn't matter, just which balls you end up with". So {1, 2, 3} would be the same as {2, 1, 3} etc.

    The probability you require is the answer to Q2 divided by the answer to Q1.
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    I do apologise, it’s a completely hypothetical question but an answer would help a real life situation. In my sons math class, 3 boys out of eight boys were chosen by their teacher to be given an opportunity to be taken to a museum. A parent complained that this was unfair - that this opportunity should have been open to everyone and not just the teachers ‘favorite’ kids. this was put to the teacher who then said he would put the names of the eight boys in class into a hat and pull three names out randomly. Incredibly, the outcome was the same ~ the names of the three boys he had originally chosen were pulled out of the hat. Of course, this was done in private. My son cried ‘fix’ so, I’d like to show him the probability of this occurring in real life.
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    (Original post by Fonda1971)
    [
    I do apologise, it’s a completely hypothetical question but an answer would help a real life situation. In my sons math class, 3 boys out of eight boys were chosen by their teacher to be given an opportunity to be taken to a museum. A parent complained that this was unfair - that this opportunity should have been open to everyone and not just the teachers ‘favorite’ kids. this was put to the teacher who then said he would put the names of the eight boys in class into a hat and pull three names out randomly. Incredibly, the outcome was the same ~ the names of the three boys he had originally chosen were pulled out of the hat. Of course, this was done in private. My son cried ‘fix’ so, I’d like to show him the probability of this occurring in real life.
    Maths forum rules are we help people to solve questions rather than tell them the answer, but I'll make an exception here...

    probaility is 1 in (8 * 7 * 6 / 6) or 1 in 56 (about 1.8%).
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    (Original post by Fonda1971)
    [
    I do apologise, it’s a completely hypothetical question but an answer would help a real life situation. In my sons math class, 3 boys out of eight boys were chosen by their teacher to be given an opportunity to be taken to a museum. A parent complained that this was unfair - that this opportunity should have been open to everyone and not just the teachers ‘favorite’ kids. this was put to the teacher who then said he would put the names of the eight boys in class into a hat and pull three names out randomly. Incredibly, the outcome was the same ~ the names of the three boys he had originally chosen were pulled out of the hat. Of course, this was done in private. My son cried ‘fix’ so, I’d like to show him the probability of this occurring in real life.
    Out of interest, what are you going to tell your son?

    1.8% is a low probability but not impossible and unlikely events happen all the time
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    Thank you so much for the answer and for making an exception. That’s great and I can now explain this in easy terms to my son. Kindest Regards.
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    And at least my son is vindicated having thought it was perhaps a fix! With a chance of 1.8% I think his hunch was right.
 
 
 
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