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Recent questions tagged counting
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find close form of generating function discrete mathematics kenneth rosen
asked
Jun 14
in
Mathematical Logic
by
sunil sarode
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52
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kennethrosen
discretemathematics
counting
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2
Combinatorics
Among the integers $1,2,3,....,200$ if $101$ integers are chosen,then show that there are two among the chosen,such that one is divisible by the other.
asked
May 29
in
Mathematical Logic
by
Sammohan Ganguly
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417
points)

49
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engineeringmathematics
discretemathematics
permutationsandcombinations
pigeonholeprinciple
counting
+1
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2
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3
Ace booklet
How many ways $4$ boys and $4$ girls can sit in a row so that no two girl are sitting side by side
asked
May 29
in
Mathematical Logic
by
Rahul singh dhakrey
(
25
points)

65
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engineeringmathematics
permutationsandcombinations
counting
discretemathematics
0
votes
1
answer
4
Combinatorics
Given m integers $a_1,a_2,....,a_m$ show that there exist integers $k,s$ with $0 \leq k < s \leq m$ such that $a_{k+1} + a_{k+2} + .....+a_s$ is divisible by $m$.
asked
May 29
in
Mathematical Logic
by
Sammohan Ganguly
(
417
points)

42
views
engineeringmathematics
discretemathematics
permutationsandcombinations
pigeonholeprinciple
counting
+1
vote
1
answer
5
Pigeonhole Principle (2)
Suppose a graph $G$ has $6$ nodes. Prove that either $G$ or $G'$ must contain a triangle. ($G'$ is the complement of $G$.) Prove it using pigeonhole principle.
asked
May 25
in
Combinatory
by
Sammohan Ganguly
(
417
points)

28
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pigeonholeprinciple
permutationsandcombinations
counting
0
votes
1
answer
6
Combinatorics
Find the number of seven digit integers with sum of the digits equal to $11$ and formed by using the digits $1,2$ and $3$ only. Soln $X_{1}+X_{2}+.......X_{7}=11$ $(x+x^{2}+x^{3})^{7}$ $(x(1+x+x^{2}))^{7}$ $x^{7}(1+x+x^{2})^{7}$ $x^{7}(\dfrac{1x^{3}}{1x})^ ... (x)3k) * ((7+k1k) xk) $((\binom{7}{k}) (x)^{3k}) \times (\binom{7+k1}{k} x^{k})$ Now not able to proceed. Kindly help.
asked
May 23
in
Combinatory
by
mbisht
(
171
points)

48
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engineeringmathematics
generatingfunctions
discretemathematics
counting
+3
votes
1
answer
7
Discrete Maths Kenneth Rosen chapter 6.3 Question 24
asked
Apr 30
in
Combinatory
by
surajumang08
(
189
points)

85
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kennethrosen
counting
permutationsandcombinations
+1
vote
3
answers
8
Counting
Show that, in a grid, the number of paths from $(0,0)$ to $(n,n)$ which does not cross ( it could touch ) the line $x = y$ is \begin{align*} \frac{1}{1+n}\binom{2\cdot n}{n} = \binom{2\cdot n}{n}  \binom{2\cdot n}{n1} \end{align*} After that, show the number of balanced paranthesis strings of length $2n$ is same as the above result.
asked
Apr 27
in
Set Theory & Algebra
by
Debashish Deka
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56.6k
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57
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counting
combinatoricsiitb
0
votes
2
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9
ISISAMPLE6
A club with $x$ members is organized into four committees such that, each member is in exactly two committees, any two committees have exactly one member in common. Then $x$ has exactly two values both between $4$ and $8$ exactly one value and this lies between $4$ and $8$ exactly two values both between $8$ and $16$ exactly one value and this lies between $8$ and $16$
asked
Mar 23
in
Mathematical Logic
by
jjayantamahata
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1.5k
points)

48
views
counting
+1
vote
2
answers
10
Counting Kenneth Rosen Exercise
How many strings with seven or more characters can be formed from the letters of the word $\text{EVERGREEN}$ ?
asked
Mar 22
in
Combinatory
by
Abhinavg
(
283
points)

165
views
discretemathematics
kennethrosen
counting
permutationsandcombinations
+4
votes
1
answer
11
Discrete Mathematics By Kenneth H Rosen Counting
asked
Mar 20
in
Combinatory
by
Sayed Athar
(
93
points)

94
views
discretemathematics
permutationsandcombinations
counting
+1
vote
0
answers
12
Number of unique solution
Suppose there is an equation $x_{1}+x_{2}+...........x_{r}=n$ Then number of unique solution in this given equation?
asked
Mar 13
in
Combinatory
by
srestha
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86.9k
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69
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counting
0
votes
1
answer
13
Rosen Example no.  9
Suppose that a computer science laboratory has $15$ workstations and $10$ servers. A cable can be used to directly connect a workstation to a server. For each server, only one direct connection to that server can be active at any time. We ... minimum number of direct connections needed to achieve this goal? Please Explain in this question how pigeonhole principle is applied .
asked
Mar 6
in
Combinatory
by
Abhinavg
(
283
points)

58
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kennethrosen
discretemathematics
counting
+1
vote
1
answer
14
Kenneth Rosen Ex.10 counting
How many ways are there to put four different employees into three indistinguishable offices when each office can contain any number of employees?
asked
Mar 2
in
Combinatory
by
Lakshman Patel RJIT
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7.7k
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102
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kennethrosen
discretemathematics
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permutationsandcombinations
+3
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1
answer
15
Combination Ex.14 Kenneth Rosen
How many bit strings of length $n$ contain exactly $r$ $1's$?
asked
Feb 28
in
Combinatory
by
Lakshman Patel RJIT
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7.7k
points)

143
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discrete
discretemathematics
kennethrosen
counting
+1
vote
2
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16
Counting problem
If I have 4 digit number formed using 5,6,7,8. What is the sum of all such 4 digit numbers? Please provide the detailed solution, I am unable to follow counting problems. Thank You.
asked
Jan 11
in
Combinatory
by
AnilGoudar
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4.5k
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92
views
discretemathematics
counting
permutationsandcombinations
+1
vote
0
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17
Counting
I am solving with Pigeon Hole Principle. Please correct me if I am wrong. Considering the required number of books as pigeons, days of the month as pigeonholes with 3 pigeons per day. if my approach is wrong, please correct me
asked
Jan 11
in
Combinatory
by
AnilGoudar
Active
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4.5k
points)

73
views
permutationsandcombinations
counting
discretemathematics
+1
vote
0
answers
18
counting
a+b+c<=12 a,b,c $\in Z^{+}$ No. of solution ?
asked
Jan 3
in
Mathematical Logic
by
vijay_jr
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1.1k
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68
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permutationsandcombinations
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discretemathematics
0
votes
4
answers
19
What is the number of ways to distribute ten identical sweets to three children?
asked
Nov 29, 2017
in
Combinatory
by
Rohit Gupta 8
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2.1k
points)

191
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permutationsandcombinations
discretemathematics
counting
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vote
0
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20
#Kenneth Rosen #Counting
Can someone explain me the solution of this problem?
asked
Nov 11, 2017
in
Set Theory & Algebra
by
MrPeppermint
(
413
points)

58
views
counting
0
votes
0
answers
21
Counting
How many ways 20 distinct numbers can be arranged in location/index 1 to 20 such that,three particular numbers(say 3,10,20) will always be present in the first half.(3,10,20 location/index will be always <11) ?
asked
Oct 29, 2017
in
Combinatory
by
rahul sharma 5
Boss
(
24.1k
points)

65
views
discretemathematics
permutationsandcombinations
counting
+2
votes
0
answers
22
P and C
Right triangle PQR is to be constructed in the xyplane so that the right angle is at P and line PR is parallel to the xaxis. The x and y coordinates of P, Q and R are to be integers that satisfy the inequalities :– $4\leq x \leq 5$ and $6\leq y \leq 16$ . How many different triangles could be constructed with these properties ? (a) 110 (b) 1,100 (c) 9,900 (d) 10,000
asked
Oct 22, 2017
in
Mathematical Logic
by
just_bhavana
Boss
(
11.9k
points)

76
views
counting
+1
vote
2
answers
23
K. Rosen: Countings
Question How many different strings of length 2 can be made from the letters in 'ORONO'? I am getting 7 strings as follows: OO, ON, OR, NO, RO, RN, NR but given answer is 6.
asked
Oct 12, 2017
in
Combinatory
by
Manu Thakur
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(
39.6k
points)

104
views
kennethrosen
discretemathematics
counting
permutationsandcombinations
+2
votes
0
answers
24
counting
Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to 15 30 90 360
asked
Jul 27, 2017
in
Graph Theory
by
set2018
Loyal
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7.6k
points)

149
views
discretemathematics
counting
+4
votes
1
answer
25
gatebook
How many bit strings of length $6$ have more no of zeros than ones?? We can solve this drawing tree but it takes so much time Is there any other way??
asked
Jul 9, 2017
in
Combinatory
by
Niharika 1
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2.1k
points)

78
views
permutationsandcombinations
counting
discretemathematics
0
votes
2
answers
26
Counting
How many ways are there to put six temporary employees into four labeled offices so that there is at least one temporary employee in each of these four offices?
asked
Jun 14, 2017
in
Mathematical Logic
by
reena_kandari
Loyal
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7.5k
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227
views
permutationsandcombinations
counting
+4
votes
2
answers
27
ISBN9780070681880  Exercise 5.3  Problem 35 (Kenneth Rosen 7ed SIE)
asked
May 27, 2017
in
Mathematical Logic
by
Rounak Agarwal
Junior
(
501
points)

144
views
kennethrosen
discretemathematics
permutationsandcombinations
counting
+2
votes
1
answer
28
counting
Number of words of 4 letters that can be formed with the letters of the word IITJEE is a) 42 b) 82 c)102 d) 142
asked
May 20, 2017
in
Probability
by
kvkumar
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(
4.9k
points)

169
views
discretemathematics
permutationsandcombinations
counting
+1
vote
0
answers
29
#rosen , #counting , #5.1 , 41(a)
in how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people , if a) the bride must next to the groom my solution is since given that bride and groom must be ... will take 5! , and arranging BG mutually is 2! , so total ways is 8c4*5!*2! but answer is given 240 (rosen )
asked
May 7, 2017
in
Combinatory
by
saket nandan
Active
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4.8k
points)

636
views
discretemathematics
counting
0
votes
2
answers
30
how to remove ambiguity that whether should take lower or upper shield in counting problem
asked
May 7, 2017
in
Mathematical Logic
by
saket nandan
Active
(
4.8k
points)

65
views
counting
discretemathematics
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