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Unformatted text preview: * 9? NO, because the two bars are identical; it doesnt matter which bar is insert rst. So, how do we count? Here is another trick: when the bars are inserted, we have 8 + 2 = 10 objects (balls + bars). Where are the bars? The bars occupy two of the 10 positions. The problem becomes clear now: we need to choose two of the 10 positions for the bars. As we learned, there are ( 10 2 ) ways to do this. Generally, if we have n balls and k bins, then we need to insert k-1 bars. There are n + k-1 objects (balls + bars). We need to choose k-1 positions for the bars. Then answer is n + k-1 k-1 . P.S. An explicit expression for S ( n, k ), Stirling number of the second kind: S ( n, k ) = 1 k ! k X j =1 (-1) k-j k j j n 1...
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This note was uploaded on 12/03/2009 for the course CSE 21 taught by Professor Graham during the Spring '07 term at UCSD.
- Spring '07