Unformatted text preview: the committee must contain more students than faculty? Binomial Theorem and Combinatorial Proofs 1. Show that n X k =0 2 k ± n k ² = 3 n 2. What is the coeﬃcient of x 3 y 5 in the expainsion of (2 x + 3 y ) 8 . Hint: be careful. .. 3. Prove that ( 2 n 2 ) = 2 ( n 2 ) + n 2 . Hint: for the RHS, break it down into cases of where the 2 elements come from. 4. A rectangular city’s roads are laid out like a grid in which (0,0) is the most southwest corner of the city and ( m,n ) is the most northeast. If there’s a road at every integer (both northsouth and eastwest), how many ways can you get from (0,0) to (m,n) assuming you never backtrack (that is, you never go south or west)? 5. Prove that ( n r )( r k ) = ( n k )( nk rk ) by using a combinatorial argument...
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 Summer '08
 STRAIN
 Permutations, Playing card, Combinatorial proofs, Rob Bayer, Rob Bayer Permutations

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