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 17bit strings are there that contain exactly 6 ones?
(b) How many 66bit strings are there that contain more ones than zeros?
(c) How many different 13card bridge hands are there? (A bridge hand is obtained by selecting 13 cards
from a standard 52card deck. The order of the cards in a bridge hand is irrelevant.)
(d) How many different 13card bridge hands are there that contain no aces?
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 Spring '08
 PAPADIMITROU
 Computer Science, Probability theory, Playing card, pancake, anagram, 13card bridge hands

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