Arranging Marbles in BoxesDate: 09/16/98 at 19:38:20 From: Chris Subject: Probability Six marbles are placed in one of three different boxes. What is the probability that each box contains two marbles? What is the formula used for this type of problem? Date: 09/17/98 at 11:21:12 From: Doctor Anthony Subject: Re: Probability You can model the situation as follows: |****| |**| where the | | represent boxes and the * are marbles. In the above diagram we have 4, 0, and 2 marbles in the three boxes, respectively. Now this diagram must begin and end with a | but otherwise the two remaining |'s and six *'s can be arranged in any order, and each of these orders is considered equally likely. So we have 8 objects to arrange in every possible way, 2 of one kind being alike and 6 of a second kind being alike. This can be done in: 8! ------ = C(8,2) = 28 ways. 2!6! [ If you haven't done permutations and combinations yet you should obtain a textbook on elementary probability and read up on the topic. It is essential knowledge for this type of question. There is also some information in this archive's FAQ to get you started. http://mathforum.org/dr.math/faq/faq.comb.perm.html ] So there are 28 possible arrangements of the marbles in the 3 boxes and only one of these will have two marbles in each box, so the required probability is: 1/28 - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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