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A question in probability

  1. Mar 2, 2006 #1
    Hey everyone
    I had difficulties while solving this problem in probability.

    We have 4 similar boxes, and 20 similar balls.
    How many possible ways we can put those balls on those boxes, knowing that
    -the first box contains 3 balls
    - the second box contains 4 balls
    - the third box contains 6 balls
    - and the fourth box contains 7 balls

    What I did, is since we have 4 boxes, it's going to be 4!
    in the first box it's 3! and second, third and fourth i also 4!*6!*7!

    So is the number of ways we can diperse those balls: 4!*4!*6!*7!

    The secong problem stats:
    How many 3-digits numbers we have that that contains 2 similar digits!
    For this one, I have NO clue how to proceed.
    Thanks for your help!
  2. jcsd
  3. Mar 2, 2006 #2
    tried calculating the ammount for 100->199 and then multiply?

    remember that 110-119 all have 2 similar and then 101 121 etc but also each set of 10 has one such as 122 assuming that it is exactly 2 similar and not 2 or more

    this is a very "ploddy" method but it will give you the correct answer, sure someone will come up with a better way soon
  4. Mar 2, 2006 #3
    I think the number canbe written as:

    then you have 4 forms {xxy, xyx, yxx, xxx} (x =! y) and x is the number that repeats itself
    than you may hav to analyse each form; for example, the first xxy
    x has 9 possibilities (from 0 to 9)
    the second x has one possibility, it should be esual to the previous x
    and the y has 9 possibilities (from 0 to 10, minus that number which x took)
    so it's, i think, 9*9*1 ???
    and u'll do so for all the other forms

    (if it says two similar, that means there may be 2 or 3 similar digits. however, if it said ONLY 2 similar, then it's 2 and nothin more)

    i am sure if this is right, because we've not learned probability yet.
  5. Mar 4, 2006 #4
    I guess I am able to solve the second problem...
    But that first one, anyone lease can help? that would be appreciated :)
  6. Mar 5, 2006 #5
    All the *balls* and *boxes* are similar. How are you supposed to differentiate between them. There will be only one arrangement possible to arrange the balls, I believe.
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