CSE-21.ProblemSet_2

CSE-21.ProblemSet_2 - or one Ace? 4. (3 pts) How many ways...

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Jonathan Thomas Guidry CSE-21 1. (4 pts) In class we learned binomial thoerem, that is n k = 0 ± n k ² x k y n - k = ( x + y ) n . By assigning values to x and y , we can obtain interesting identi- ties. In the following identities, indicate which values of x and y that should be assigned: (a) n k = 0 ( n k ) = 2 n x = , y = 1 (b) b n / 2 c k = 0 ( n 2 k ) = b ( n - 1 ) / 2 c k = 0 ( n 2 k + 1 ) x = , y = 1 (c) n k = 0 2 k ( n k ) = 3 n x = , y = 1 (d) 2 m k = 0 ( - 1 ) k ( 4 m 2 k ) = ( - 4 ) m ( Hint: Use your imagination !) x = , y = 1 2. (3 pts) How many ways can 25 identical jellybeans be distributed to 5 boys and 4 girls if: (a) there is no restriction; (b) if every boy gets at least one jellybean and every girl gets at least two ; (c) if no boy gets more than 1 jellybean. 3. (3 pts) How many different 5-card poker hands from an ordinary deck of 52 cards are there: (a) which contain no spades; (b) which contain at least one heart; (c) which contain at least one heart
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Unformatted text preview: or one Ace? 4. (3 pts) How many ways can a group of 4 men and 4 women be split into 4 (possibly unequal) non-empty teams if: (a) there is no restriction; (b) no team can have more than 4 people; (c) each team must have at least one man and at least one woman. 5. (2 pts) How many different words can be made from rear-ranging all 14 of the letters of SCHWARZENEGGER, but using no more of each letter than it occurs; e.g., you can only use 2 Rs)? What if we only want to form 3-letter words? Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 1...
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This note was uploaded on 04/23/2008 for the course CSE 21 taught by Professor Graham during the Spring '07 term at UCSD.

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