Six marbles are placed in one of three different boxes. What

Make sure u know abt these methods for these kind of problems:

1) no of ways in which n things can be divided among r persons so that each of them can receive 0 or more is n+r-1Cr-1.

2) no of ways in which n things can be divided among r persons so that each of them receive at least 1 is n-1Cr-1

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!

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