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Recent questions in Combinatory
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Combinatorics:
Counting,
Recurrence relations,
Generating functions.
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1
Combinatorics
There are 100 students. 85 choose Math, 80 choose Physics, 75 choose Chemistry, 70 choose Biology. What is the minimum number of students choosing all 4 subjects? Assume each student chosen at least one subject?
asked
2 days
ago
in
Combinatory
by
aditi19
(
201
points)

16
views
permutationsandcombinations
+1
vote
1
answer
2
Rosen book Generating Functions pg no 430
asked
3 days
ago
in
Combinatory
by
anip
(
33
points)

18
views
kennethrosen
generatingfunctions
discretemathematics
#counting
+1
vote
2
answers
3
Permutations with restrictions
$Z =\left \{ {A,B,C,D,E,F,G} \right \}$ How many permutations of all elements of set $Z$ are possible when A cannot appear after D and C cannot appear after F C cannot appear after D
asked
Jul 31
in
Combinatory
by
Mk Utkarsh
Boss
(
14k
points)

63
views
permutationsandcombinations
discretemathematics
0
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
(
613
points)

88
views
counting
+1
vote
1
answer
5
Discrete mathematics Kenneth Rosen excersise 6.1 q4
asked
Jul 28
in
Combinatory
by
Sandy Sharma
Junior
(
677
points)

32
views
kennethrosen
discretemathematics
0
votes
1
answer
6
Kenneth H. Rosen 7th edition 5.5
How many ways are there to distribute five balls into three boxes if each box must have atleast one ball in it and if the balls are labelled but the boxes are unlabelled?
asked
Jul 28
in
Combinatory
by
snehasarkar
(
39
points)

31
views
0
votes
1
answer
7
Permutations
The number of permutations of ‘n’ different things taken not more than ‘r’ at a time, with repetitions being allowed, is (a) (nr – 1)/ (n – 1) (b) (nr – 1) / (n – 1)! (c) n(nr – 1)/ (n – 1) (d) (nr – 1) / n!
asked
Jul 25
in
Combinatory
by
shubham6596
(
163
points)

35
views
permutationsandcombinations
0
votes
0
answers
8
How it is possible?
[closed]
asked
Jul 24
in
Combinatory
by
cool_dude
(
73
points)

20
views
discretemathematics
0
votes
0
answers
9
Combinatorics
asked
Jul 23
in
Combinatory
by
HeadShot
Junior
(
657
points)

33
views
0
votes
1
answer
10
Linear Recurrence relations
$\text{What is the general form of homogeneous solution for linear nonhomogeneous recurrence relation }$ $a_n = 8 a_{n2}  16a_{n4}$
asked
Jul 22
in
Combinatory
by
!KARAN
(
415
points)

19
views
recurrence
0
votes
3
answers
11
Combinatorics
A company hires 11 new employees, each of whom is to be assigned to one of 4 subdivisions. Each subdivision will get at least one new employee. In how many ways can these assignments be made?
asked
Jul 22
in
Combinatory
by
krishn.jh
Junior
(
743
points)

138
views
permutationsandcombinations
+1
vote
1
answer
12
Generating Function Where to start?
Hello can anyone suggest good video/book to learn generating functions from?..i tried the nptel lecture..it has some audio lag. and i could not make much out of it..I am well versed in combinatorics but my calculus is weak.. Please suggest some resource that teaches generating functions from scratch
asked
Jul 19
in
Combinatory
by
Tridhara Chakrabarti
(
255
points)

57
views
generatingfunctions
preparation
+1
vote
2
answers
13
Engineering mathematics
$\text{How many 5 letter word can be formed}$ $\text{from 6 a's,6 b's,6 c's,5 d's,5e's,4f's,4g's,3h's,3i's ?}$
asked
Jul 15
in
Combinatory
by
Shivani gaikawad
(
331
points)

50
views
engineeringmathematics
zeal
permutationsandcombinations
0
votes
3
answers
14
Self Doubt
How to evaluate this quickly? $\large\sum^{20}_{r=0}(1)^r\binom{r+2}{r}\\OR\\\large\sum^{20}_{r=0}(1)^r(r+2)(r+1)$
asked
Jul 11
in
Combinatory
by
Soumya29
Boss
(
12.3k
points)

83
views
permutationsandcombinations
0
votes
0
answers
15
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?
[closed]
asked
Jul 6
in
Combinatory
by
Balaji Jegan
Active
(
1.4k
points)

44
views
permutationsandcombinations
counting
discretemathematics
+1
vote
1
answer
16
Rosen(Generating combination)
I am not getting this condition. Can someone please explain that condition with that example.
asked
Jul 5
in
Combinatory
by
tusharp
Junior
(
813
points)

49
views
discretemathematics
kennethrosen
0
votes
1
answer
17
Rosen (Combinatorics)
I am not getting this. Can someone please explain using example. Thank you
asked
Jul 5
in
Combinatory
by
tusharp
Junior
(
813
points)

69
views
discretemathematics
kennethrosen
permutationsandcombinations
0
votes
1
answer
18
Rosen(PnC)
Suppose we consider n=4 and r=2 then bit string formed is like b1,b2,b3,b4 where Bi is bit. Now to ensure exactly two 1's in any of these 4 places we can do it byc(4,2). After this suppose string look like 1,b2,b3,1 now for remaining two bits, each has (n1) options as we want exactly two 1's. so how could just C(n,r) is used here?
asked
Jul 5
in
Combinatory
by
tusharp
Junior
(
813
points)

35
views
kennethrosen
discretemathematics
permutationsandcombinations
0
votes
0
answers
19
Rosen Pigeonhole principle
Not getting highlighted part how ceil N/K will be greater or equal to r?
[closed]
asked
Jul 4
in
Combinatory
by
tusharp
Junior
(
813
points)

13
views
pigeonholeprinciple
0
votes
0
answers
20
Question regarding Catalan Number
I have a question regarding Catalan Number. The question is as follows, Find the number of binary strings w of length 2n with an equal number of 1’s and 0’s and the property that every prefix of w has at least as many as 0’s as 1’s. Now i know the answer for this question is 2nCn/(n+1). I wanted to know how this question relates to Catalan number?
asked
Jul 1
in
Combinatory
by
noxevolution
(
23
points)

43
views
discretemathematics
permutationsandcombinations
0
votes
0
answers
21
Rosen Discrete Maths book. Recurrence Relations. Example #3
asked
Jun 29
in
Combinatory
by
Abhisek Das
Active
(
1.3k
points)

13
views
+1
vote
1
answer
22
The minimum no of comparisons required to find minimum and maximum of 100 numbers is __
asked
Jun 29
in
Combinatory
by
Rishav Kumar Singh
Active
(
2.3k
points)

35
views
testseries
0
votes
1
answer
23
combinatorics
let say there are three elements in a set {1,2,3}.find total #of 4 digit no. which are neither non decreasing nor non increasing.
asked
Jun 28
in
Combinatory
by
Aman Juyal
(
269
points)

46
views
permutationsandcombinations
0
votes
4
answers
24
CombinatoricsKenneth Rosen(Ex 6.611)
In how many different ways can seven different jobs be assigned to four different employees so that each employee is assigned at least one job and the most difficult job is assigned to the best employee? I got the first point that we need to ... set with 4 elements. But how to deal with the second part that most difficult job is assigned to the best employee?
asked
Jun 28
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

161
views
discretemathematics
inclusionexclusion
kennethrosen
0
votes
2
answers
25
CombinatoricsKenneth Rosen(Ex 6.5)
How many bit strings of length eight do not contain six consecutive 0's?
asked
Jun 26
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

76
views
discretemathematics
kennethrosen
inclusionexclusion
0
votes
1
answer
26
Combinatorics kenneth Rosen(ex 6.4 47e)
asked
Jun 26
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

105
views
kennethrosen
generatingfunctions
discretemathematics
0
votes
1
answer
27
CombinatoricsKenneth Rosen (Ex6.445)
Find a closed form for the exponential generating function for the sequence $\{ a_n \}$ where $a_n=\frac{1}{n+1}$ and the exponential generating function for the sequence $\{a_n\}$ is the series $\sum_{n=0}^{\infty}\frac{a_n}{n!}x^n$
asked
Jun 26
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

88
views
discretemathematics
generatingfunctions
kennethrosen
0
votes
0
answers
28
Combinatorics  Kenneth Rosen(Ex 6.4 7c)
asked
Jun 25
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

45
views
kennethrosen
generatingfunctions
discretemathematics
0
votes
1
answer
29
CombinatoricsKenneth Rosen(Ex 5.341)
How many ways are there for a horse race with three horses to finish if ties are possible.(Two or three horses may tie).
asked
Jun 24
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

25
views
discretemathematics
permutationsandcombinations
0
votes
2
answers
30
CombinatoricsKenneth Rosen(Ex 5.3 31)
The english alphabet contains 21 consonants and five vowels.How many strings of six lowercase letters of the English alphabet contain (b)Exactly two vowels (d)At least two vowels For (b) part I solved it like choose 2 vowels from 5 in $\binom{5}{2}$ ways ... }*6!))$ and both of my answers don't match with the key in Rosen. Please let me know where I am wrong.
asked
Jun 24
in
Combinatory
by
Ayush Upadhyaya
Boss
(
11k
points)

64
views
discretemathematics
kennethrosen
permutationsandcombinations
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