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2225
Kenneth Rosen Edition 7 Exercise 6.2 Question 9 (Page No. 405)
What is the minimum number of students, each of whom comes from one of the $50$ states, who must be enrolled in a university to guarantee that there are at least $100$ who come from the same state?
What is the minimum number of students, each of whom comes from one of the $50$ states, who must be enrolled in a university to guarantee that there are at least $100$ wh...
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2227
Kenneth Rosen Edition 7 Exercise 6.2 Question 7 (Page No. 405)
Let $n$ be a positive integer. Show that in any set of $n$ consecutive integers there is exactly one divisible by $n.$
Let $n$ be a positive integer. Show that in any set of $n$ consecutive integers there is exactly one divisible by $n.$
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2228
Kenneth Rosen Edition 7 Exercise 6.2 Question 6 (Page No. 405)
Let $d$ be a positive integer. Show that among any group of $d + 1$ (not necessarily consecutive) integers there are two with exactly the same remainder when they are divided by $d.$
Let $d$ be a positive integer. Show that among any group of $d + 1$ (not necessarily consecutive) integers there are two with exactly the same remainder when they are div...
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2229
Kenneth Rosen Edition 7 Exercise 6.2 Question 5 (Page No. 405)
Show that among any group of five (not necessarily consecutive) integers, there are two with the same remainder when divided by $4.$
Show that among any group of five (not necessarily consecutive) integers, there are two with the same remainder when divided by $4.$
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2232
Kenneth Rosen Edition 7 Exercise 6.2 Question 2 (Page No. 405)
Show that if there are $30$ students in a class, then at least two have last names that begin with the same letter.
Show that if there are $30$ students in a class, then at least two have last names that begin with the same letter.
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2233
Kenneth Rosen Edition 7 Exercise 6.2 Question 1 (Page No. 405)
Show that in any set of six classes, each meeting regularly once a week on a particular day of the week, there must be two that meet on the same day, assuming that no classes are held on weekends.
Show that in any set of six classes, each meeting regularly once a week on a particular day of the week, there must be two that meet on the same day, assuming that no cla...
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2234
Kenneth Rosen Edition 7 Exercise 6.1 Question 65 (Page No. 398)
How many ways are there to arrange the letters $a, b, c,\:\text{and}\: d$ such that $a$ is not followed immediately by $b?$
How many ways are there to arrange the letters $a, b, c,\:\text{and}\: d$ such that $a$ is not followed immediately by $b?$
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2235
Kenneth Rosen Edition 7 Exercise 6.1 Question 64 (Page No. 398)
Use a tree diagram to find the number of bit strings of length four with no three consecutive $0s.$
Use a tree diagram to find the number of bit strings of length four with no three consecutive $0s.$
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2236
Kenneth Rosen Edition 7 Exercise 6.1 Question 63 (Page No. 398)
Use the principle of inclusion–exclusion to find the number of positive integers less than $1,000,000$ that are not divisible by either $4\:\text{or}\: \text{by}\: 6.$
Use the principle of inclusion–exclusion to find the number of positive integers less than $1,000,000$ that are not divisible by either $4\:\text{or}\: \text{by}\: 6.$
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2237
Kenneth Rosen Edition 7 Exercise 6.1 Question 61 (Page No. 398)
A wired equivalent privacy (WEP) key for a wireless fidelity (WiFi) network is a string of either $10, 26,\:\text{or}\: 58$ hexadecimal digits. How many different WEP keys are there?
A wired equivalent privacy (WEP) key for a wireless fidelity (WiFi) network is a string of either $10, 26,\:\text{or}\: 58$ hexadecimal digits. How many different WEP key...
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2239
Kenneth Rosen Edition 7 Exercise 6.1 Question 53 (Page No. 398)
How many positive integers not exceeding $100$ are divisible either by $4$ or by $6?$
How many positive integers not exceeding $100$ are divisible either by $4$ or by $6?$
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2240
Kenneth Rosen Edition 7 Exercise 6.1 Question 50 (Page No. 398)
How many bit strings of length $10$ contain either five consecutive $0s$ or five consecutive $1s?$
How many bit strings of length $10$ contain either five consecutive $0s$ or five consecutive $1s?$
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