Mathematics for Computer Science
14.11. References 593 Problem 14.6. (a)How many of the billion numbers in the range from 1 to 109 contain the digit 1? (Hint:How ...
Chapter 14 Cardinality Rules594 1 3 7 5 4 2 6 65622 tree code 1 2 3 4 5 432 Figure 14.7 (a)Describe a procedure for reconstructi ...
14.11. References 595 Describe a bijection fromBXto the set of permutations ofX.^7 This implies that there are how may bijection ...
Chapter 14 Cardinality Rules596 matter which way they face. We’ll be interested in counting how many arrange- ments there are of ...
14.11. References 597 (a)Your TA has a list of the 12 students in front of him, so he divides the list into consecutive groups o ...
Chapter 14 Cardinality Rules598 (b)Anr-permutationof a set is a sequence ofrdistinct elements of that set. For example, here are ...
14.11. References 599 Problem 14.21. Answer the following questions with a number or a simple formula involving fac- torials and ...
Chapter 14 Cardinality Rules600 the ranks.r 3 ;r 4 ;r 5 /of the remaining three cards, listed in increasing suit order where | ...
14.11. References 601 (a)For how many rolls doexactlytwo dice have the value 6 and the remaining five dice all have different va ...
Chapter 14 Cardinality Rules602 consisting ofkrooted trees. To add the next edge, we choose any vertex to be the root of a new t ...
14.11. References 603 O 2 BO 1 K KO 2 BO 1 O 1 BO 2 K KO 1 BO 2 BO 1 O 2 K BO 2 O 1 K ::: BOOK OBOK KOBO ::: (d)What kind of map ...
Chapter 14 Cardinality Rules604 Problems for Section 14.6 Practice Problems Problem 14.27. How many different permutations are t ...
14.11. References 605 Theoccurrence numberfor a character in a word is the number of times that the character occurs in the word ...
Chapter 14 Cardinality Rules606 A set of two edges that share a vertex is called anincident pair(i.p.); the shared vertex is cal ...
14.11. References 607 Problems for Section 14.7 Practice Problems Problem 14.33. Indicate how many 5-card hands there are of eac ...
Chapter 14 Cardinality Rules608 (b)How many lengthmwords can be formed from ann-letter alphabet, if letters can be reused? (c)Ho ...
14.11. References 609 (c)At least 3 people were born on the same day of the week. (d)At least 4 people were born in the same mon ...
Chapter 14 Cardinality Rules610 Hint:Hall’s Theorem and degree-constrained (11.5.5) graphs. Problem 14.40. The Magician can dete ...
14.11. References 611 are determined to find a way to make a trick like this work. They decide to change the rules slightly: ins ...
Chapter 14 Cardinality Rules612 Exam Problems Problem 14.45. A standard 52 card deck has 13 cards of each suit. Use the Pigeonho ...
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