Recent questions and answers in Combinatory

0 votes

0 answers

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

0 votes

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

answered 4 days ago in Combinatory by Soumya29 Active (5.2k points) | 63 views

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0 answers

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

0 votes

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.

answered 6 days ago in Combinatory by Mk Utkarsh Boss (11.7k points) | 48 views

+1 vote

1 answer

5

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

answered Apr 13 in Combinatory by Subarna Das Active (2.7k points) | 56 views

0 votes

0 answers

6

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

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

0 votes

1 answer

8

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

answered Apr 12 in Combinatory by pankaj_vir Loyal (6.3k points) | 93 views

+3 votes

1 answer

9

Test Series

answered Apr 12 in Combinatory by ankitgupta.1729 Active (4.2k points) | 138 views

0 votes

1 answer

10

Indistinguishable objects and Indistinguishable boxes

answered Apr 7 in Combinatory by Soumya29 Active (5.2k points) | 58 views

+1 vote

1 answer

11

Permutations

answered Apr 6 in Combinatory by Tesla! Boss (15.1k points) | 78 views

+6 votes

3 answers

12

ISI 2004 MIII
The number of permutation of {1,2,3,4,5} that keep at least one integer fixed is. 81 76 120 60

answered Apr 6 in Combinatory by yash789 (27 points) | 293 views

+1 vote

2 answers

13

Kenneth Rosen (Special Indian Edition) Section 6.1 Exercise Problem #9d

answered Apr 4 in Combinatory by pankaj_vir Loyal (6.3k points) | 203 views

+1 vote

2 answers

14

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

answered Apr 2 in Combinatory by pankaj_vir Loyal (6.3k points) | 51 views

+10 votes

5 answers

15

ISI 2004 MIII
In how many ways can three person, each throwing a single die once, make a score of 11 22 27 24 38

answered Apr 1 in Combinatory by Hitesh (289 points) | 501 views

0 votes

1 answer

16

Kenneth Rosen Recurrence Relation Example 8

answered Apr 1 in Combinatory by abhishekmehta4u Loyal (9.1k points) | 84 views

+1 vote

2 answers

17

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?

answered Mar 31 in Combinatory by pankaj_vir Loyal (6.3k points) | 96 views

+25 votes

7 answers

18

GATE 2016-1-27
Consider the recurrence relation $a_1 =8 ,a_n =6n^2 +2n+a_{n-1}.$ Let $a_{99}=K\times 10^4$. The value of $K$ is __________.

answered Mar 31 in Combinatory by pankaj_vir Loyal (6.3k points) | 4.8k views

+24 votes

5 answers

19

GATE2015-1_26
$\sum\limits_{x=1}^{99}\frac{1}{x(x+1)}$ = __________________.

answered Mar 31 in Combinatory by pankaj_vir Loyal (6.3k points) | 1.4k views

+3 votes

2 answers

20

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?

answered Mar 26 in Combinatory by ankitgupta.1729 Active (4.2k points) | 88 views

+24 votes

8 answers

21

GATE2014-1-49
A pennant is a sequence of numbers, each number being 1 or 2. An $n$-pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a 4-pennant. The set of all possible 1-pennants is ${(1)}$, the set of all possible 2-pennants is ${(2), (1,1 ... ,1,1), (1,2)}$. Note that the pennant $(1,2)$ is not the same as the pennant $(2,1)$. The number of 10-pennants is________

answered Mar 24 in Combinatory by Prateek K Active (1.2k points) | 1.7k views

+1 vote

2 answers

22

Counting Kenneth Rosen Exercise
How many strings with seven or more characters can be formed from the letters of the word $\text{EVERGREEN}$ ?

answered Mar 22 in Combinatory by Sukanya Das Boss (11.2k points) | 113 views

+4 votes

1 answer

23

Discrete Mathematics By Kenneth H Rosen Counting

answered Mar 20 in Combinatory by Sukanya Das Boss (11.2k points) | 78 views

+4 votes

2 answers

24

Combination (Repetition)
A girl has to choose 4 items from a bucket which contains 3 red, 3 green, and 4 blue balls, now in how many ways she can do this?

answered Mar 19 in Combinatory by akshat sharma Active (1.5k points) | 103 views

0 votes

0 answers

25

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

+1 vote

5 answers

26

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? $6$ $36$ $72$ $90$

answered Mar 18 in Combinatory by Shivam14chd (107 points) | 116 views

+3 votes

2 answers

27

Permutation and combination
in how many ways 2 alike apple, 3 alike orange and 4 alike mango can be given to 3 children if each child can have none or 1 or more than 1 fruits.

answered Mar 17 in Combinatory by Shivam14chd (107 points) | 106 views

0 votes

0 answers

28

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

0 votes

0 answers

29

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

0 votes

1 answer

30

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 .

answered Mar 6 in Combinatory by Deepakk Poonia (Dee) Active (2.8k points) | 43 views

0 votes

0 answers

31

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

0 votes

0 answers

32

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

+2 votes

2 answers

33

rosen exercise problem
How many bit strings of length 10 contain at least three 1s and at least three 0s? My Approach:-> using product rule There are 3 subtask following (filling 3 ones in 10 places) = (filling 3 zeros in remaing 7 places) = (filling remaining 4 places) = ... ** which is greater than (total number of string). Now , i want to know what is wrong in my apporach. please explain..

answered Mar 3 in Combinatory by monanshi Loyal (9.4k points) | 301 views

+1 vote

1 answer

34

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?

answered Mar 2 in Combinatory by Sukanya Das Boss (11.2k points) | 88 views

+2 votes

2 answers

35

Permutation and Combination
A train has 12 stations on it's route and it has to stopped at any 4 station, such that no two stations are consecutive. find number of possible way for choosing 4 station's?

answered Mar 1 in Combinatory by Mk Utkarsh Boss (11.7k points) | 81 views

+3 votes

1 answer

36

Combination Ex.14 Kenneth Rosen
How many bit strings of length $n$ contain exactly $r$ $1's$?

answered Mar 1 in Combinatory by Sukanya Das Boss (11.2k points) | 119 views

0 votes

3 answers

37

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.

answered Feb 25 in Combinatory by gari Active (3.2k points) | 142 views

+1 vote

1 answer

38

Generating function doubt
Please give me clarification

answered Feb 24 in Combinatory by Sukannya Active (2.6k points) | 222 views

+15 votes

4 answers

39

TIFR2010-A-12
The coefficient of $x^{3}$ in the expansion of $(1 + x)^{3} (2 + x^{2})^{10}$ is. $2^{14}$ $31$ $\left ( \frac{3}{3} \right ) + \left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) + 2\left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) \left ( \frac{10}{1} \right ) 2^{9}$

answered Feb 24 in Combinatory by Lakshman Patel RJIT Loyal (7.5k points) | 520 views

+2 votes

0 answers

40

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

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author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true

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