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Recent questions tagged counting
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1
Counting
1)In how many ways we can put n distinct balls in k identical bins? 2)In how many ways we can put n distinct balls in k identical bins such that no bin is empty?
asked
Sep 15
in
Probability
by
srestha
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96.1k
points)

56
views
discretemathematics
counting
0
votes
2
answers
2
testbook series
Number of ways of arranging the word "TESTBOOK" such that E always comes between O's.
asked
Sep 6
in
Combinatory
by
TUSHAR_BHATT
(
315
points)

44
views
permutationsandcombinations
counting
testbooktestseries
0
votes
2
answers
3
PigeonHole Principal
A drawer contains a dozen of brown and dozen of black socks,all unmatched.A man takes socks out at random in the dark. How many socks must he take out to be sure that he has atleast two black socks ?
asked
Sep 3
in
Mathematical Logic
by
Na462
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5.7k
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18
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pigeonholeprinciple
permutationsandcombinations
counting
+2
votes
1
answer
4
MADEEASY
Consider a set S={1000,1001,1002........,9999}. The numbers in set S having atleast one digit as 2 and atleast one digit as 5 are?
asked
Jul 29
in
Combinatory
by
Utkarsh Joshi
Junior
(
653
points)

119
views
counting
0
votes
0
answers
5
Combinatorics Question on Bit Strings
How many bit strings of length 8 contain either three consecutive 0's or four consecutive 1's ? MY APPROACH : Initially, for 3 consecutive 0's: 000_ _ _ _ _ =>2^5 = 32 WAYS 1000_ _ _ _ =>2^4 = 16 WAYS _1000_ _ _ =>2^4 = 16 WAYS _ _1000_ ... =>2*3! = 12 WAYS so, total ways = 112 + 48  12 = 148 ways But answer is given as 147 ways. Where am I wrong?
asked
Jul 6
in
Combinatory
by
Balaji Jegan
Active
(
1.7k
points)

49
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permutationsandcombinations
counting
discretemathematics
+3
votes
1
answer
6
find close form of generating function discrete mathematics kenneth rosen
asked
Jun 14
in
Mathematical Logic
by
sunil sarode
Active
(
1.3k
points)

87
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kennethrosen
discretemathematics
counting
0
votes
1
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7
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
(
435
points)

73
views
engineeringmathematics
discretemathematics
permutationsandcombinations
pigeonholeprinciple
counting
+2
votes
2
answers
8
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
(
35
points)

82
views
engineeringmathematics
permutationsandcombinations
counting
discretemathematics
0
votes
1
answer
9
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
(
435
points)

55
views
engineeringmathematics
discretemathematics
permutationsandcombinations
pigeonholeprinciple
counting
+1
vote
1
answer
10
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
(
435
points)

44
views
pigeonholeprinciple
permutationsandcombinations
counting
0
votes
1
answer
11
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
(
265
points)

66
views
engineeringmathematics
generatingfunctions
discretemathematics
counting
+3
votes
1
answer
12
Discrete Maths Kenneth Rosen chapter 6.3 Question 24
asked
Apr 30
in
Combinatory
by
surajumang08
(
189
points)

101
views
kennethrosen
counting
permutationsandcombinations
+2
votes
4
answers
13
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
Veteran
(
57.2k
points)

88
views
counting
combinatoricsiitb
0
votes
2
answers
14
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)

54
views
counting
+1
vote
2
answers
15
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
(
351
points)

187
views
discretemathematics
kennethrosen
counting
permutationsandcombinations
+4
votes
1
answer
16
Discrete Mathematics By Kenneth H Rosen Counting
asked
Mar 20
in
Combinatory
by
Sayed Athar
(
93
points)

110
views
discretemathematics
permutationsandcombinations
counting
+1
vote
0
answers
17
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
Veteran
(
96.1k
points)

78
views
counting
0
votes
1
answer
18
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
(
351
points)

64
views
kennethrosen
discretemathematics
counting
+1
vote
2
answers
19
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
Loyal
(
8k
points)

152
views
kennethrosen
discretemathematics
counting
permutationsandcombinations
+3
votes
1
answer
20
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
Loyal
(
8k
points)

156
views
discrete
discretemathematics
kennethrosen
counting
+1
vote
2
answers
21
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
Active
(
4.5k
points)

100
views
discretemathematics
counting
permutationsandcombinations
+1
vote
0
answers
22
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
(
4.5k
points)

75
views
permutationsandcombinations
counting
discretemathematics
+1
vote
0
answers
23
counting
a+b+c<=12 a,b,c $\in Z^{+}$ No. of solution ?
asked
Jan 3
in
Mathematical Logic
by
vijay_jr
Active
(
1.1k
points)

69
views
permutationsandcombinations
counting
discretemathematics
0
votes
4
answers
24
What is the number of ways to distribute ten identical sweets to three children?
asked
Nov 29, 2017
in
Combinatory
by
Rohit Gupta 8
Active
(
2.1k
points)

233
views
permutationsandcombinations
discretemathematics
counting
+1
vote
0
answers
25
#Kenneth Rosen #Counting
Can someone explain me the solution of this problem?
asked
Nov 11, 2017
in
Set Theory & Algebra
by
MrPeppermint
(
473
points)

62
views
counting
0
votes
0
answers
26
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
(
24.7k
points)

66
views
discretemathematics
permutationsandcombinations
counting
+2
votes
0
answers
27
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
(
12k
points)

80
views
counting
+1
vote
2
answers
28
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
Boss
(
40.2k
points)

110
views
kennethrosen
discretemathematics
counting
permutationsandcombinations
+2
votes
0
answers
29
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
(
7.9k
points)

154
views
discretemathematics
counting
+4
votes
1
answer
30
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
Active
(
2.1k
points)

84
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permutationsandcombinations
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