Introductory Combinatorics
Introductory Combinatorics
5th Edition
ISBN: 9780136020400
Author: Richard A. Brualdi
Publisher: Prentice Hall
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Chapter 11, Problem 53E
To determine

To prove: A graph is a tree if and only if it does not contain any cycles, but the insertion of any new edge always creates exactly one cycle.

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Answer this two questions: 2 . We roll seven 20-sided dice, numbered 1 to 20. Show that it is always possible to find two disjoint nonempty subsets of the dice such that the sums of the shown faces of the dice in each of the subsets coincide(only one of the faces is considered to be shown) .   4. We are given a deck of 60 cards, 40 are identical black cards, 10 are identical red cards, and 10 are identical greenc ards. How may ways are there to deal the 60 cards to three distinct players so that everyone gets exactly 20 cards?
The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The accompanying data represent the pH in samples of bottled water and tap water. Complete parts (a) and (b). Click the icon to view the data table. (a) Determine the mean, median, and mode pH for each type of water. Comment on the differences between the two water types. Select the correct choice below and fill in any answer boxes in your choice. A. For tap water, the mean pH is (Round to three decimal places as needed.) B. The mean does not exist. Data table Тар Bottled 7.64 7.45 7.46 7.50 7.68 7.45 7.10 7.56 7.46 7.52 5.15 5.09 5.31 5.20 4.78 5.52 5.31 5.13 5.31 5.21 7.69 7.46 5.23 5.24 Print Done - ☑
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Introductory Combinatorics

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