document.write( "Question 1143349: How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable but the boxes are not? \n" ); document.write( "

Algebra.Com's Answer #764158 by math_helper(2461) $\"\"$ $\"About$

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document.write( "The case of indistinguishable boxes requires Stirling's number of the 2nd kind (this arises due to a recursive nature of combinations: you put ball A into a box, then ball B can go into the box with A or one of the other two boxes, etc.):\r
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document.write( "S(n,k) = Stirling's number of the 2nd kind
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document.write( "S(n,k) = \r
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document.write( "        with C(k,j) = k!/((k-j)!j!) \r
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document.write( "We have  n=6 balls, k=3 boxes.  You can distribute the balls into one box, into two boxes, or all three boxes: \r
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document.write( "S(6,1) + S(6,2) + S(6,3) = 1 + 31 + 90 =  \r
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