ex7 - CS70 Discrete Mathematics for Computer Science,...

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CS70 Discrete Mathematics for Computer Science, Spring 2012 Homework 7 Out: 8 March. Due: 5pm, 15 March. Instructions: Start each problem on a new sheet. Write your name, section number and “CS70” on every sheet. If you use more than one sheet for a problem, staple them together (but do not staple different problems together). Put your solutions in the boxes on Soda level 2 by 5pm on Thursday: your solution to Q1 goes in box CS70–1, your solution to Q2 goes in box CS70–2, and so on ( five boxes total). You are encouraged to form small groups (two to four people) to work through the homework, but you must write up all your solutions on your own. 1. Counting, counting and counting The only way to learn counting is to practice, practice, practice, so here is your chance to do so. You should leave your answers as (tidy) expressions involving factorials, binomial coefficients etc., rather than evaluating them as decimal numbers (though you are welcome to perform this last step as well for your own interest if you like, provided it is clearly separated from your main answer). Also, you should explain clearly how you arrived at your answers; bald solutions with no explanation will receive no credit. (a) How many 17-bit strings are there that contain exactly 6 ones? (b) How many 66-bit strings are there that contain more ones than zeros? (c) How many different 13-card bridge hands are there? (A bridge hand is obtained by selecting 13 cards from a standard 52-card deck. The order of the cards in a bridge hand is irrelevant.) (d) How many different 13-card bridge hands are there that contain no aces?
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This note was uploaded on 03/18/2012 for the course CS 70 taught by Professor Papadimitrou during the Spring '08 term at University of California, Berkeley.

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ex7 - CS70 Discrete Mathematics for Computer Science,...

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