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6.5 Worksheet (5.3: Counting bit strings. re there subject to each of the following restrictions? H. 6.4 Worksheet Exercise 6.4.1: Counting functions from a set to itself. Count the number of different functions with the given domain, target and additional properties. (a) f: {0,1}7 (0, 1}". (b) f: {0,1}7 {0,1}. The function f is one-to-one. (c) f: {0,1}5 → {0,1}7. (d) f: {0,1}5→ {0,1}7. The function f is one-to-one. queto Exercise 6.4.2: Counting telephone numbers. At a certain university in the U.S., all phone numbers are 7-digits long and start with either 824 or 825. (a) How many different phone numbers are possible? 140M (b) How many different phone numbers are there in which the last four digits are all different? Exercise 6.4.3: Lining up a wedding party for a photo. Ten members of a wedding party are lining up in a row for a photograph. (a) How many ways are there to line up the ten people? Page 1 of 2 6.5 Worksheet (5.3: Counting bit strings. re there subject to each of the following restrictions? H. 6.4 Worksheet Exercise 6.4.1: Counting functions from a set to itself. Count the number of different functions with the given domain, target and additional properties. (a) f: {0,1}7 (0, 1}". (b) f: {0,1}7 {0,1}. The function f is one-to-one. (c) f: {0,1}5 → {0,1}7. (d) f: {0,1}5→ {0,1}7. The function f is one-to-one. queto Exercise 6.4.2: Counting telephone numbers. At a certain university in the U.S., all phone numbers are 7-digits long and start with either 824 or 825. (a) How many different phone numbers are possible? 140M (b) How many different phone numbers are there in which the last four digits are all different? Exercise 6.4.3: Lining up a wedding party for a photo. Ten members of a wedding party are lining up in a row for a photograph. (a) How many ways are there to line up the ten people? Page 1 of 2

6.5 Worksheet (5.3: Counting bit strings. re there subject to each of the following restrictions? H. 6.4 Worksheet Exercise 6.4.1: Counting functions from a set to itself. Count the number of different functions with the given domain, target and additional properties. (a) f: {0,1}7 (0, 1}". (b) f: {0,1}7 {0,1}. The function f is one-to-one. (c) f: {0,1}5 → {0,1}7. (d) f: {0,1}5→ {0,1}7. The function f is one-to-one. queto Exercise 6.4.2: Counting telephone numbers. At a certain university in the U.S., all phone numbers are 7-digits long and start with either 824 or 825. (a) How many different phone numbers are possible? 140M (b) How many different phone numbers are there in which the last four digits are all different? Exercise 6.4.3: Lining up a wedding party for a photo. Ten members of a wedding party are lining up in a row for a photograph. (a) How many ways are there to line up the ten people? Page 1 of 2 6.5 Worksheet (5.3: Counting bit strings. re there subject to each of the following restrictions? H. 6.4 Worksheet Exercise 6.4.1: Counting functions from a set to itself. Count the number of different functions with the given domain, target and additional properties. (a) f: {0,1}7 (0, 1}". (b) f: {0,1}7 {0,1}. The function f is one-to-one. (c) f: {0,1}5 → {0,1}7. (d) f: {0,1}5→ {0,1}7. The function f is one-to-one. queto Exercise 6.4.2: Counting telephone numbers. At a certain university in the U.S., all phone numbers are 7-digits long and start with either 824 or 825. (a) How many different phone numbers are possible? 140M (b) How many different phone numbers are there in which the last four digits are all different? Exercise 6.4.3: Lining up a wedding party for a photo. Ten members of a wedding party are lining up in a row for a photograph. (a) How many ways are there to line up the ten people? Page 1 of 2

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 1TFE: True or False Label each of the following statement as either true or false. 1. Parity check...
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6.5 Worksheet (5.3: Counting bit strings. re there subject to each of the following restrictions? H. 6.4 Worksheet Exercise 6.4.1: Counting functions from a set to itself. Count the number of different functions with the given domain, target and additional properties. (a) f: {0,1}7 (0, 1}". (b) f: {0,1}7 {0,1}. The function f is one-to-one. (c) f: {0,1}5 → {0,1}7. (d) f: {0,1}5→ {0,1}7. The function f is one-to-one. queto Exercise 6.4.2: Counting telephone numbers. At a certain university in the U.S., all phone numbers are 7-digits long and start with either 824 or 825. (a) How many different phone numbers are possible? 140M (b) How many different phone numbers are there in which the last four digits are all different? Exercise 6.4.3: Lining up a wedding party for a photo. Ten members of a wedding party are lining up in a row for a photograph. (a) How many ways are there to line up the ten people? Page 1 of 2
Transcribed Image Text:6.5 Worksheet (5.3: Counting bit strings. re there subject to each of the following restrictions? H. 6.4 Worksheet Exercise 6.4.1: Counting functions from a set to itself. Count the number of different functions with the given domain, target and additional properties. (a) f: {0,1}7 (0, 1}". (b) f: {0,1}7 {0,1}. The function f is one-to-one. (c) f: {0,1}5 → {0,1}7. (d) f: {0,1}5→ {0,1}7. The function f is one-to-one. queto Exercise 6.4.2: Counting telephone numbers. At a certain university in the U.S., all phone numbers are 7-digits long and start with either 824 or 825. (a) How many different phone numbers are possible? 140M (b) How many different phone numbers are there in which the last four digits are all different? Exercise 6.4.3: Lining up a wedding party for a photo. Ten members of a wedding party are lining up in a row for a photograph. (a) How many ways are there to line up the ten people? Page 1 of 2
6.5 Worksheet (5.3: Counting bit strings. re there subject to each of the following restrictions? H. 6.4 Worksheet Exercise 6.4.1: Counting functions from a set to itself. Count the number of different functions with the given domain, target and additional properties. (a) f: {0,1}7 (0, 1}". (b) f: {0,1}7 {0,1}. The function f is one-to-one. (c) f: {0,1}5 → {0,1}7. (d) f: {0,1}5→ {0,1}7. The function f is one-to-one. queto Exercise 6.4.2: Counting telephone numbers. At a certain university in the U.S., all phone numbers are 7-digits long and start with either 824 or 825. (a) How many different phone numbers are possible? 140M (b) How many different phone numbers are there in which the last four digits are all different? Exercise 6.4.3: Lining up a wedding party for a photo. Ten members of a wedding party are lining up in a row for a photograph. (a) How many ways are there to line up the ten people? Page 1 of 2
Transcribed Image Text:6.5 Worksheet (5.3: Counting bit strings. re there subject to each of the following restrictions? H. 6.4 Worksheet Exercise 6.4.1: Counting functions from a set to itself. Count the number of different functions with the given domain, target and additional properties. (a) f: {0,1}7 (0, 1}". (b) f: {0,1}7 {0,1}. The function f is one-to-one. (c) f: {0,1}5 → {0,1}7. (d) f: {0,1}5→ {0,1}7. The function f is one-to-one. queto Exercise 6.4.2: Counting telephone numbers. At a certain university in the U.S., all phone numbers are 7-digits long and start with either 824 or 825. (a) How many different phone numbers are possible? 140M (b) How many different phone numbers are there in which the last four digits are all different? Exercise 6.4.3: Lining up a wedding party for a photo. Ten members of a wedding party are lining up in a row for a photograph. (a) How many ways are there to line up the ten people? Page 1 of 2
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