Unformatted text preview: 8. In bridge, each of 4 players is dealt 13 cards from a standard 52card deck. How many diﬀerent possibilities are there for such a setup? 9. 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. 10. Prove that ( n + r +1 r ) = ( n ) + ( n +1 1 ) + ( n +2 2 ) + ··· ( n + r r ) . Hint: the RHS counts the number of ways to give r indistinguishable objects to n + 2 people. 11. 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)? 12. Prove that ( n r )( r k ) = ( n k )( nk rk ) by using a combinatorial argument...
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This note was uploaded on 09/10/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.
 Summer '08
 STRAIN
 Math

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