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 ﬁgure out what is or isn’t 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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 Summer '09
 RobBayer
 Math, Natural number, standard 52card deck, Rob Bayer

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