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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 non-negative 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