Recent questions in Combinatory

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1

#Pigeonhole Principle Doubt
How many positive integers not exceeding 1000 are divisible by 7? So, the doubt here is why we are taking floor function while calculating this .

asked 3 days ago in Combinatory by Abhinavg (127 points) | 36 views

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2 answers

2

GATE question
Q. 6 Xs has to be placed in the figure below such that each row contains at least one X. In how many ways can this be done? a) 160 b) 180 c) 170 d) 26

asked 4 days ago in Combinatory by Sachin Kumar Verma (49 points) | 63 views

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3

Combinations with 3 Jugs
You are given 3 jugs A,B and C of capacities 8, 5 and 3 liters, respectively. A is filled and B and C are empty. Total amount of water is 8 liters. How many different combinations are possible with at least one of the jug being empty or at-least one of them being full. For example $(8,0,0)$ , $(4,4,0)$ , $(5,3,0)$ [closed]

asked 5 days ago in Combinatory by Mk Utkarsh Boss (11.7k points) | 52 views

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1 answer

4

Combinatorics
How many ways we can move from a point (a,b) to a point (i,j) in a coordinate system. Here i>a and j>b and at each step you can move to the right or in the upward direction.

asked 5 days ago in Combinatory by Kushagra Chatterjee Junior (647 points) | 48 views

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5

COMBINATRICS
NUMBER OF WAYS IN WHICH CORNER OF THE SQUARE CAN BE COLORED WITH TWO COLORS. (ITS IS PERMISSIBLE TO USE A SINGLE COLOUR ON ALL FOUR CORNER)

asked Apr 13 in Combinatory by Ismail Junior (599 points) | 42 views

+1 vote

1 answer

6

COMBINATRICS
NUMBER OF WAYS WE CAN ARRAYS LETTERS OF THE WORD "TESTBOOK" SO THAT NO TWO VOWELS ARE TOGETHER IS

asked Apr 13 in Combinatory by Ismail Junior (599 points) | 56 views

+1 vote

0 answers

7

Permutation of 4 Gs out of 5 Gs
Given symbols:- $GGGGGAAATTTECCS$ No of ways such that exactly 4 Gs out of 5 Gs are together. I am getting$ \frac{11! × 11}{3!×3!×2!} $. Some one verify it?

asked Apr 12 in Combinatory by Jason Active (1.2k points) | 94 views

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1 answer

8

Kenneth Rosen, Generating Functions, Exercise - 6.4 QNO-33

asked Apr 12 in Combinatory by Abhinavg (127 points) | 93 views

+1 vote

1 answer

9

Permutations

asked Apr 4 in Combinatory by shivanisrivarshini Boss (14k points) | 78 views

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1 answer

10

Indistinguishable objects and Indistinguishable boxes

asked Apr 4 in Combinatory by Na462 Active (1.6k points) | 58 views

+1 vote

2 answers

11

Kenneth Rosen , Recurrence relation, Exercise 6.1 Qno. - 19

asked Apr 2 in Combinatory by Abhinavg (127 points) | 51 views

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1 answer

12

Kenneth Rosen Recurrence Relation Example 8

asked Mar 31 in Combinatory by Abhinavg (127 points) | 84 views

+1 vote

2 answers

13

Generating functions
What will be the coefficient of x^17 in the expansion of (x+x^2+x^3+x^4+x^5+x^6)^4?

asked Mar 29 in Combinatory by Mayank Khakharia 1 (29 points) | 96 views

+3 votes

2 answers

14

Combinatorics
Sanjay have 9 distinct paths (1,2,3.....,9) from his home to his work place. He works from Monday to Friday every week, he does not go to work on Saturdays and Sundays. Every Sunday he schedules that which path he will take for each ... The only restriction is that he cannot select even number paths on 2 consecutive days. How many possible combinations he have to make his schedule?

asked Mar 26 in Combinatory by Mk Utkarsh Boss (11.7k points) | 88 views

+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 (127 points) | 112 views

+4 votes

1 answer

16

Discrete Mathematics By Kenneth H Rosen Counting

asked Mar 20 in Combinatory by Sayed Athar (93 points) | 78 views

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17

self doubt
Three men have 4 coats, 5 waist coats, and 6 caps. In how many ways can they wear them? Three men have 4 coats, 5 waist coats, and 6 caps. In how many ways can they wear any type of them?

asked Mar 18 in Combinatory by Kaluti Loyal (5.3k points) | 34 views

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18

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 (81.7k points) | 60 views

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19

sheldon ross
Three balls are to be randomly selected without replacement from an urn containing $20$ balls numbered $1$ through $20$. If we bet that at least one of the balls that are drawn has a number as large as or larger than $17$, what is the probability that we win the bet?

asked Mar 10 in Combinatory by Ananya Jaiswal 1 Active (1.2k points) | 59 views

+1 vote

5 answers

20

Combinatorics
Three ladies have each brought a child for admission to a school. The head of the school wishes to interview the six people one by one, taking care that no child is interviewed before its mother. In how many different ways can the interviews be arranged? $6$ $36$ $72$ $90$

asked Mar 8 in Combinatory by Junaed Siddiquee (179 points) | 116 views

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1 answer

21

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 (127 points) | 43 views

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22

Composition of function
"f:A->B & g:C->D are 2 functions then for their composition B should be equal to C." But if B is not equal to C then composition is possible or not? Eg:A={1,2,} B={3,4} C={4,5} D={6,7} then can fog be computed Or not? f={(1,3), (2,4)} g={(4,6),(5,7)} gof={(2,6)} is it true or not? I hope my question could be understood:) [closed]

asked Mar 3 in Combinatory by MayankSharma (121 points) | 27 views

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23

Combinatorics
There are total 21 identical balls in a shop and 7 children. In how many ways can 7 children claim the balls? (it is not necessary to claim all the balls)

asked Mar 3 in Combinatory by Mk Utkarsh Boss (11.7k points) | 79 views

+1 vote

1 answer

24

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 (7.5k points) | 88 views

+3 votes

1 answer

25

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 (7.5k points) | 118 views

+1 vote

1 answer

26

Generating function doubt
Please give me clarification

asked Feb 24 in Combinatory by Lakshman Patel RJIT Loyal (7.5k points) | 222 views

+2 votes

0 answers

27

Extended Binomial Coefficients
Find the value of extended Binomial Coefficient $\binom{-1/2}{3}$

asked Feb 24 in Combinatory by Mk Utkarsh Boss (11.7k points) | 67 views

0 votes

3 answers

28

Self doubt generating function
Equation: $x+y=10$ and we are asked to find out the number of a non-negative integral solution of this equation.

asked Feb 23 in Combinatory by Lakshman Patel RJIT Loyal (7.5k points) | 142 views

+1 vote

2 answers

29

Sheldon Ross
From 10 married couples, we want to select group of 6 that is not allowed to contain a married couple. How many choices are there?

asked Feb 20 in Combinatory by Tesla! Boss (15.1k points) | 68 views

+2 votes

1 answer

30

Sheldon Ross
Prove $\binom{m+n}{r}$ = $\binom{n}{0}\binom{m}{r}+\binom{n}{1}\binom{m}{r-1}+... +\binom{n}{r}\binom{m}{0}$

asked Feb 20 in Combinatory by Tesla! Boss (15.1k points) | 54 views

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