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Unformatted text preview: there for such a setup? 5. How many ways can you split a set of n elements into 2 disjoint subsets? Note: there is a very short and simple formula for this. Also, YOU need to gure out what is or isnt labelled (or distinguishable) in this problem. 6. How many solutions in nonnegative integers are there to (a) x 1 + x 2 + x 3 + x 4 + x 5 = 30 and x 1 10? (b) x 1 + x 2 + x 3 + x 4 30? (Hint: where did x 5 go? I miss it. ..) 7. F Prove that ( n + r +1 r ) = ( n ) + ( n +1 1 ) + ( n +2 2 ) + ( n + r r ) . Hint: the LHS counts the number of ways to split r identical coins among n + 2 people....
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This note was uploaded on 02/06/2012 for the course MATHEMATIC 55 taught by Professor Robbayer during the Summer '09 term at University of California, Berkeley.
 Summer '09
 RobBayer
 Math

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