Unformatted text preview: 8. In bridge, each of 4 players is dealt 13 cards from a standard 52-card 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 north-south and east-west), 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 )( n-k r-k ) 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