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Recent questions tagged kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 31 (Page No. 414)
The English alphabet contains $21$ consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain exactly one vowel? exactly two vowels? at least one vowel? at least two vowels?
The English alphabet contains $21$ consonants and five vowels. How many strings of six lowercase letters of the English alphabet containexactly one vowel?exactly two vowe...
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1.5k
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 30 (Page No. 414)
Seven women and nine men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of five members of the department if at least one woman must be on the committee? How many ... of five members of the department if at least one woman and at least one man must be on the committee?
Seven women and nine men are on the faculty in the mathematics department at a school.How many ways are there to select a committee of five members of the department if a...
admin
4.1k
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 29 (Page No. 414)
How many $4$-permutations of the positive integers not exceeding $100$ contain three consecutive integers $k, k + 1, k + 2,$ in the correct order where these consecutive integers can perhaps be separated by other integers in the permutation? where they are in consecutive positions in the permutation?
How many $4$-permutations of the positive integers not exceeding $100$ contain three consecutive integers $k, k + 1, k + 2,$ in the correct orderwhere these consecutive i...
admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 28 (Page No. 414)
A professor writes $40$ discrete mathematics true/false questions. Of the statements in these questions, $17$ are true. If the questions can be positioned in any order, how many different answer keys are possible?
A professor writes $40$ discrete mathematics true/false questions. Of the statements in these questions, $17$ are true. If the questions can be positioned in any order, h...
admin
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admin
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Apr 29, 2020
Combinatory
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Kenneth Rosen Edition 7 Exercise 6.3 Question 27 (Page No. 414)
A club has $25$ members. How many ways are there to choose four members of the club to serve on an executive committee? How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office?
A club has $25$ members.How many ways are there to choose four members of the club to serve on an executive committee?How many ways are there to choose a president, vice ...
admin
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 26 (Page No. 414)
Thirteen people on a softball team show up for a game. How many ways are there to choose $10$ players to take the field? How many ways are there to assign the $10$ positions by selecting players from the $13$ people who show ... ways are there to choose $10$ players to take the field if at least one of these players must be a woman?
Thirteen people on a softball team show up for a game.How many ways are there to choose $10$ players to take the field?How many ways are there to assign the $10$ position...
admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 25 (Page No. 414)
One hundred tickets, numbered $1, 2, 3,\dots, 100,$ are sold to $100$ different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). How many ways are there to award the prizes if there ... $73 \: \text{and}\: 97$ do not win prizes?
One hundred tickets, numbered $1, 2, 3,\dots, 100,$ are sold to $100$ different people for a drawing. Four different prizes are awarded, including a grand prize (a trip t...
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4.7k
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Apr 29, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 6.3 Question 24 (Page No. 414)
How many ways are there for $10$ women and six men to stand in a line so that no two men stand next to each other? [Hint: First position the women and then consider possible positions for the men.]
How many ways are there for $10$ women and six men to stand in a line so that no two men stand next to each other? [Hint: First position the women and then consider possi...
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1.0k
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 23 (Page No. 414)
How many ways are there for eight men and five women to stand in a line so that no two women stand next to each other? [Hint: First position the men and then consider possible positions for the women.]
How many ways are there for eight men and five women to stand in a line so that no two women stand next to each other? [Hint: First position the men and then consider pos...
admin
737
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 22 (Page No. 414)
How many permutations of the letters $\text{ABCDEFGH}$ contain the string $\text{ED}?$ the string $\text{CDE}?$ the strings $\text{BA and FGH}?$ the strings $\text{AB, DE, and GH}?$ the strings $\text{CAB and BED}?$ the strings $\text{BCA and ABF}?$
How many permutations of the letters $\text{ABCDEFGH}$ containthe string $\text{ED}?$the string $\text{CDE}?$the strings $\text{BA and FGH}?$ the strings $\text{AB, DE, a...
admin
6.2k
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 21 (Page No. 414)
How many permutations of the letters $\text{ABCDEFG}$ contain the string $\text{BCD}?$ the string $\text{CFGA}? $ the strings $\text{BA and GF}? $ the strings $\text{ABC and DE}? $ the strings $\text{ABC and CDE}?$ the strings $\text{CBA and BED}?$
How many permutations of the letters $\text{ABCDEFG}$ containthe string $\text{BCD}?$ the string $\text{CFGA}? $the strings $\text{BA and GF}? $the strings $\text{ABC and...
admin
6.3k
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admin
asked
Apr 29, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 6.3 Question 20 (Page No. 413)
How many bit strings of length $10$ have exactly three $0s?$ more $0s$ than $1s?$ at least seven $1s?$ at least three $1s?$
How many bit strings of length $10$ haveexactly three $0s?$ more $0s$ than $1s?$at least seven $1s?$ at least three $1s?$
admin
1.8k
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admin
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Apr 29, 2020
Combinatory
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Kenneth Rosen Edition 7 Exercise 6.3 Question 19 (Page No. 413)
A coin is flipped $10$ times where each flip comes up either heads or tails. How many possible outcomes are there in total? contain exactly two heads? contain at most three tails? contain the same number of heads and tails?
A coin is flipped $10$ times where each flip comes up either heads or tails. How many possible outcomesare there in total?contain exactly two heads?contain at most three ...
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3.5k
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 18 (Page No. 413)
A coin is flipped eight times where each flip comes up either heads or tails. How many possible outcomes are there in total? contain exactly three heads? contain at least three heads? contain the same number of heads and tails?
A coin is flipped eight times where each flip comes up either heads or tails. How many possible outcomesare there in total?contain exactly three heads?contain at least th...
admin
1.8k
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admin
asked
Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 17 (Page No. 413)
How many subsets with more than two elements does a set with $100$ elements have?
How many subsets with more than two elements does a set with $100$ elements have?
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571
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 16 (Page No. 413)
How many subsets with an odd number of elements does a set with $10$ elements have?
How many subsets with an odd number of elements does a set with $10$ elements have?
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 15 (Page No. 413)
In how many ways can a set of five letters be selected from the English alphabet?
In how many ways can a set of five letters be selected from the English alphabet?
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474
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 14 (Page No. 413)
In how many ways can a set of two positive integers less than $100$ be chosen?
In how many ways can a set of two positive integers less than $100$ be chosen?
admin
610
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admin
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Apr 29, 2020
Combinatory
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Kenneth Rosen Edition 7 Exercise 6.3 Question 13 (Page No. 413)
A group contains $n$ men and $n$ women. How many ways are there to arrange these people in a row if the men and women alternate?
A group contains $n$ men and $n$ women. How many ways are there to arrange these people in a row if the men and women alternate?
admin
507
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Apr 29, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 6.3 Question 12 (Page No. 413)
How many bit strings of length $12$ contain exactly three $1s?$ at most three $1s?$ at least three $1s?$ an equal number of $0s\: \text{and}\: 1s?$
How many bit strings of length $12$ containexactly three $1s?$ at most three $1s?$ at least three $1s?$ an equal number of $0s\: \text{and}\: 1s?$
admin
1.8k
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 6.3 Question 11 (Page No. 413)
How many bit strings of length $10$ contain exactly four $1s?$ at most four $1s?$ at least four $1s?$ an equal number of $0s$ and $1s?$
How many bit strings of length $10$ containexactly four $1s?$at most four $1s?$at least four $1s?$an equal number of $0s$ and $1s?$
admin
13.5k
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 6.3 Question 10 (Page No. 413)
There are six different candidates for governor of a state. In how many different orders can the names of the candidates be printed on a ballot?
There are six different candidates for governor of a state. In how many different orders can the names of the candidates be printed on a ballot?
admin
1.3k
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 9 (Page No. 413)
How many possibilities are there for the win, place, and show (first, second, and third) positions in a horse race with $12$ horses if all orders of finish are possible?
How many possibilities are there for the win, place, and show (first, second, and third) positions in a horse race with $12$ horses if all orders of finish are possible?
admin
416
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admin
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Apr 29, 2020
Combinatory
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Kenneth Rosen Edition 7 Exercise 6.3 Question 8 (Page No. 413)
In how many different orders can five runners finish a race if no ties are allowed?
In how many different orders can five runners finish a race if no ties are allowed?
admin
350
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 7 (Page No. 413)
Find the number of $5$-permutations of a set with nine elements.
Find the number of $5$-permutations of a set with nine elements.
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366
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Apr 29, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 6.3 Question 6 (Page No. 413)
Find the value of each of these quantities. $C(5, 1)$ $C(5, 3)$ $C(8, 4)$ $C(8, 8)$ $C(8, 0)$ $C(12, 6)$
Find the value of each of these quantities.$C(5, 1)$$C(5, 3)$$C(8, 4)$$C(8, 8)$$C(8, 0)$$C(12, 6)$
admin
378
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 5 (Page No. 413)
Find the value of each of these quantities. $P (6, 3)$ $P (6, 5)$ $P (8, 1)$ $P (8, 5)$ $P (8, 8)$ $P (10, 9)$
Find the value of each of these quantities.$P (6, 3)$$P (6, 5)$$P (8, 1)$$P (8, 5)$$P (8, 8)$$P (10, 9)$
admin
1.5k
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admin
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 4 (Page No. 413)
Let $S = \{1, 2, 3, 4, 5\}.$ List all the $3$-permutations of $S$. List all the $3$-combinations of $S.$
Let $S = \{1, 2, 3, 4, 5\}.$List all the $3$-permutations of $S$.List all the $3$-combinations of $S.$
admin
284
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Apr 29, 2020
Combinatory
kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 6.3 Question 3 (Page No. 413)
How many permutations of $\{a, b, c, d, e, f, g\}$ end with $a?$
How many permutations of $\{a, b, c, d, e, f, g\}$ end with $a?$
admin
274
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admin
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Apr 29, 2020
Combinatory
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Kenneth Rosen Edition 7 Exercise 6.3 Question 2 (Page No. 413)
How many different permutations are there of the set $\{a, b, c, d, e, f, g\}?$
How many different permutations are there of the set $\{a, b, c, d, e, f, g\}?$
admin
255
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admin
asked
Apr 29, 2020
Combinatory
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