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Recent questions tagged kennethrosen
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Kenneth Rosen Edition 7th Exercise 6.5 Question 59 (Page No. 434)
How many ways are there to distribute five balls into three boxes if each box must have at least one ball in it if both the balls and boxes are labeled? the balls are labeled, but the boxes are unlabeled? the balls are unlabeled, but the boxes are labeled? both the balls and boxes are unlabeled?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

11
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
2
Kenneth Rosen Edition 7th Exercise 6.5 Question 58 (Page No. 434)
How many ways are there to distribute five balls into seven boxes if each box must have at most one ball in it if both the balls and boxes are labeled? the balls are labeled, but the boxes are unlabeled? the balls are unlabeled, but the boxes are labeled? both the balls and boxes are unlabeled?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

10
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
3
Kenneth Rosen Edition 7th Exercise 6.5 Question 57 (Page No. 434)
How many ways are there to pack nine identical DVDs into three indistinguishable boxes so that each box contains at least two DVDs?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

6
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
4
Kenneth Rosen Edition 7th Exercise 6.5 Question 56 (Page No. 434)
How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

9
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
5
Kenneth Rosen Edition 7th Exercise 6.5 Question 55 (Page No. 434)
How many ways are there to distribute six indistinguishable objects into four indistinguishable boxes so that each of the boxes contains at least one object?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

10
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
6
Kenneth Rosen Edition 7th Exercise 6.5 Question 54 (Page No. 434)
How many ways are there to distribute five indistinguishable objects into three indistinguishable boxes?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

8
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
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answers
7
Kenneth Rosen Edition 7th Exercise 6.5 Question 53 (Page No. 434)
How many ways are there to put six temporary employees into four identical offices so that there is at least one temporary employee in each of these four offices?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

7
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
8
Kenneth Rosen Edition 7th Exercise 6.5 Question 52 (Page No. 434)
How many ways are there to put five temporary employees into four identical offices?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

6
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
9
Kenneth Rosen Edition 7th Exercise 6.5 Question 51 (Page No. 434)
How many ways are there to distribute six distinguishable objects into four indistinguishable boxes so that each of the boxes contains at least one object?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

6
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
10
Kenneth Rosen Edition 7th Exercise 6.5 Question 50 (Page No. 434)
How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

10
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
11
Kenneth Rosen Edition 7th Exercise 6.5 Question 49 (Page No. 433  434)
In this exercise we will prove Theorem $2$ by setting up a onetoone correspondence between the set of $r$combinations with repetition allowed of $S = \{1, 2, 3,\dots,n\}$ and the set of $r$ ... that there are $C(n + r − 1,r)\:\: r$combinations with repetition allowed from a set with n elements.
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

11
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
12
Kenneth Rosen Edition 7th Exercise 6.5 Question 48 (Page No. 433)
Prove Theorem $4$ by first setting up a onetoone correspondence between permutations of $n$ objects with $n_{i}$ indistinguishable objects of type $i,\; i = 1, 2, 3,\dots, k,$ and the distributions of $n$ objects in $k$ boxes such that $n_{i}$ objects are placed in box $i,\: i = 1, 2, 3,\dots,k $ and then applying Theorem $3.$
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

5
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
13
Kenneth Rosen Edition 7th Exercise 6.5 Question 47 (Page No. 433)
Use the product rule to prove Theorem $4,$ by first placing objects in the first box, then placing objects in the second box, and so on.
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

6
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
14
Kenneth Rosen Edition 7th Exercise 6.5 Question 46 (Page No. 433)
A shelf holds $12$ books in a row. How many ways are there to choose five books so that no two adjacent books are chosen? [Hint: Represent the books that are chosen by bars and the books not chosen by stars. Count the number of sequences of five bars and seven stars so that no two bars are adjacent.]
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

7
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
15
Kenneth Rosen Edition 7th Exercise 6.5 Question 45 (Page No. 433)
How many ways can n books be placed on k distinguishable shelves if the books are indistinguishable copies of the same title? if no two books are the same, and the positions of the books on the shelves matter?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

5
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
16
Kenneth Rosen Edition 7th Exercise 6.5 Question 44 (Page No. 433)
In how many ways can a dozen books be placed on four distinguishable shelves if the books are indistinguishable copies of the same title? if no two books are the same, and the positions of the books on the shelves matter? [Hint: Break this into $12$ ... $b_{2}, b_{3},\dots, \text{and }\:b_{12}.]$
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

4
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
17
Kenneth Rosen Edition 7th Exercise 6.5 Question 43 (Page No. 433)
How many ways are there to deal hands of five cards to each of six players from a deck containing $48$ different cards?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

10
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
18
Kenneth Rosen Edition 7th Exercise 6.5 Question 42 (Page No. 433)
In bridge, the $52$ cards of a standard deck are dealt to four players. How many different ways are there to deal bridge hands to four players?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

12
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
19
Kenneth Rosen Edition 7th Exercise 6.5 Question 41 (Page No. 433)
How many ways are there to deal hands of seven cards to each of five players from a standard deck of $52$ cards?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

12
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
0
answers
20
Kenneth Rosen Edition 7th Exercise 6.5 Question 40 (Page No. 433)
How many ways are there to travel in $xyzw$ space from the origin $(0, 0, 0, 0)$ to the point $(4, 3, 5, 4)$ by taking steps one unit in the positive $x,$ positive $y,$ positive $z,$ or positive $w$ direction?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

6
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
21
Kenneth Rosen Edition 7th Exercise 6.5 Question 39 (Page No. 433)
How many ways are there to travel in $xyz$ space from the origin $(0, 0, 0)$ to the point $(4, 3, 5)$ by taking steps one unit in the positive $x$ direction, one unit in the positive $y$ direction, or one unit ... direction? (Moving in the negative $x, y,\: \text{or}\: z$ direction is prohibited, so that no backtracking is allowed.)
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

15
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
22
Kenneth Rosen Edition 7th Exercise 6.5 Question 38 (Page No. 433)
A professor packs her collection of $40$ issues of a mathematics journal in four boxes with $10$ issues per box. How many ways can she distribute the journals if each box is numbered, so that they are distinguishable? the boxes are identical, so that they cannot be distinguished?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

11
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
23
Kenneth Rosen Edition 7th Exercise 6.5 Question 37 (Page No. 433)
A student has three mangos, two papayas, and two kiwi fruits. If the student eats one piece of fruit each day, and only the type of fruit matters, in how many different ways can these fruits be consumed?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

17
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
24
Kenneth Rosen Edition 7th Exercise 6.5 Question 36 (Page No. 433)
How many different bit strings can be formed using six $1s$ and eight $0s?$
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

12
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
25
Kenneth Rosen Edition 7th Exercise 6.5 Question 35 (Page No. 433)
How many strings with seven or more characters can be formed from the letters in $\text{EVERGREEN}?$
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

10
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
26
Kenneth Rosen Edition 7th Exercise 6.5 Question 34 (Page No. 433)
How many strings with five or more characters can be formed from the letters in $\text{SEERESS}?$
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

12
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
27
Kenneth Rosen Edition 7th Exercise 6.5 Question 33 (Page No. 433)
How many different strings can be made from the letters in $\text{ORONO},$ using some or all of the letters?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

10
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
28
Kenneth Rosen Edition 7th Exercise 6.5 Question 32 (Page No. 433)
How many different strings can be made from the letters in $\text{AARDVARK},$ using all the letters, if all three $As$ must be consecutive?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

10
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
29
Kenneth Rosen Edition 7th Exercise 6.5 Question 31 (Page No. 433)
How many different strings can be made from the letters in $\text{ABRACADABRA,}$ using all the letters?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

9
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
0
votes
1
answer
30
Kenneth Rosen Edition 7th Exercise 6.5 Question 30 (Page No. 433)
How many different strings can be made from the letters in $\text{MISSISSIPPI},$ using all the letters?
asked
May 1
in
Combinatory
by
Lakshman Patel RJIT

10
views
kennethrosen
discretemathematics
counting
combinatory
descriptive
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