Recent questions in Combinatory

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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

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1 answer

2

Rosen book Generating Functions pg no 430

asked 3 days ago in Combinatory by anip (33 points) | 18 views

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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

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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

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1 answer

5

Discrete mathematics Kenneth Rosen excersise 6.1 q4

asked Jul 28 in Combinatory by Sandy Sharma Junior (677 points) | 32 views

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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

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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

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8

How it is possible?
[closed]

asked Jul 24 in Combinatory by cool_dude (73 points) | 20 views

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9

Combinatorics

asked Jul 23 in Combinatory by HeadShot Junior (657 points) | 33 views

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1 answer

10

Linear Recurrence relations
$\text{What is the general form of homogeneous solution for linear nonhomogeneous recurrence relation }$ $a_n = 8 a_{n-2} - 16a_{n-4}$

asked Jul 22 in Combinatory by !KARAN (415 points) | 19 views

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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

+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

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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

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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

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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

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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

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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

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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 (n-1) 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

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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

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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

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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

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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

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4 answers

24

Combinatorics-Kenneth Rosen(Ex 6.6-11)
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

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2 answers

25

Combinatorics-Kenneth 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

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1 answer

26

Combinatorics- kenneth Rosen(ex 6.4 47e)

asked Jun 26 in Combinatory by Ayush Upadhyaya Boss (11k points) | 105 views

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1 answer

27

Combinatorics-Kenneth Rosen (Ex6.4-45)
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

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0 answers

28

Combinatorics - Kenneth Rosen(Ex 6.4 7c)

asked Jun 25 in Combinatory by Ayush Upadhyaya Boss (11k points) | 45 views

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1 answer

29

Combinatorics-Kenneth Rosen(Ex 5.3-41)
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

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2 answers

30

Combinatorics-Kenneth 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

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