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Recent questions tagged discrete-mathematics

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482
Kenneth Rosen Edition 7 Exercise 6.3 Question 36 (Page No. 414)
How many bit strings contain exactly five $0s$ and $14\:\: 1s$ if every $0$ must be immediately followed by two $1s?$
How many bit strings contain exactly five $0s$ and $14\:\: 1s$ if every $0$ must be immediately followed by two $1s?$
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483
Kenneth Rosen Edition 7 Exercise 6.3 Question 35 (Page No. 414)
How many bit strings contain exactly eight $0s$ and $10\:\: 1s$ if every $0$ must be immediately followed by a $1?$
How many bit strings contain exactly eight $0s$ and $10\:\: 1s$ if every $0$ must be immediately followed by a $1?$
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484
Kenneth Rosen Edition 7 Exercise 6.3 Question 34 (Page No. 414)
Suppose that a department contains $10$ men and $15$ women. How many ways are there to form a committee with six members if it must have more women than men?
Suppose that a department contains $10$ men and $15$ women. How many ways are there to form a committee with six members if it must have more women than men?
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485
Kenneth Rosen Edition 7 Exercise 6.3 Question 33 (Page No. 414)
Suppose that a department contains $10$ men and $15$ women. How many ways are there to form a committee with six members if it must have the same number of men and women?
Suppose that a department contains $10$ men and $15$ women. How many ways are there to form a committee with six members if it must have the same number of men and women?...
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494
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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495
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...
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1 answer
498
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 $1s?$
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1 answer
505
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?
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1 answer
506
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 $0s\: \text{and}\: 1s?$
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507
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 $1s?$
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1 answer
508
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?
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509
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?
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