Recent questions in Combinatory

0 votes

0 answers

1

self doubt
number of integers in the set {0,1,2,3......,10000}which contain digit 5 exactly once ???? i got the 9*9*9*9 is it right???

asked 2 days ago in Combinatory by vijju532 (61 points) | 23 views

0 votes

0 answers

2

Random
There are 6 pairs of black socks and 6 pairs of white socks.What is the probability to pick a pair of black or white socks when 2 socks are selected randomly in darkness. My thoughts: Since there have asked for probability to pick a "pair", we must consider those ... 6C1)/ 24C2 + (6C1 * 6C1)/ 24C2 = 6/23 Which is the correct approach and why? Why am I getting different results? [closed]

asked Jun 5 in Combinatory by Warlock lord Active (3.4k points) | 31 views

0 votes

1 answer

3

Mind Boggling question

asked Jun 3 in Combinatory by Balaji Jegan Active (1.1k points) | 79 views

0 votes

1 answer

4

Ace booklet
The minimum number of non negative integers we have to choose randomly so that there will be atleast two integers x and y such that x+y or x-y is divisible by 10

asked May 30 in Combinatory by Rahul singh dhakrey (25 points) | 20 views

0 votes

2 answers

5

#Combinatorics
#COMB There are $4$ boys and $6$ prizes are to be distributed among them such that each has at least $1$ prize. How many ways that can be done? My solution: $\text{Case 1 : 3 1 1 1}$ $\text{Case 2 : 2 2 1 11}$ $\text{Case 1 : C(6, ... My doubt is in the second case, am I not considering the prizes to be indistinguishable? I am confused in this regard. Please help me clear this doubt.

asked May 25 in Combinatory by Abhisek Das Active (1.3k points) | 77 views

+1 vote

1 answer

6

Pigeonhole Principle (3)
Let $a_1,a_2,a_3,....a_{100}$ and $b_1,b_2,b_3,....b_{100}$ be any two permutations of the integers from $1$ to $100$. $a_1b_1,a_2b_2,a_3b_3,....,a_{100}b_{100}$ Prove that among the $100$ products given above there are two products whose difference is divisible by $100$.

asked May 25 in Combinatory by Sammohan Ganguly (417 points) | 48 views

+1 vote

1 answer

7

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 (417 points) | 27 views

+2 votes

1 answer

8

Pigeon hole (1)
Prove that out of hundred whole numbers one will always have $15$ of them such that the difference between any two of these $15$ numbers is divisible by $7$.

asked May 25 in Combinatory by Sammohan Ganguly (417 points) | 30 views

+1 vote

1 answer

9

Pigeon hole
Show that in a group of $n$ people there are two who have identical number of friends in that group.

asked May 25 in Combinatory by Sammohan Ganguly (417 points) | 28 views

0 votes

1 answer

10

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{1-x^{3}}{1-x})^ ... (-x)3k) * ((7+k-1k) xk) $((\binom{7}{k}) (-x)^{3k}) \times (\binom{7+k-1}{k} x^{k})$ Now not able to proceed. Kindly help.

asked May 23 in Combinatory by mbisht (161 points) | 47 views

0 votes

1 answer

11

query about partitionproblems in combinatorics

asked May 22 in Combinatory by mbisht (161 points) | 33 views

0 votes

2 answers

12

ISI-MTECH-CSE-2018
One needs to choose six real numbers $x_1,x_2,....,x_6$ such that the product of any five of them is equal to other number. The number of such choices is $3$ $33$ $63$ $93$

asked May 20 in Combinatory by jjayantamahata Active (1.5k points) | 158 views

+1 vote

4 answers

13

kennneth rosen chapter- counting
1. Find the coefficient of $x^{10}$ in the power series. $\left ( 1+x^{2}+x^{4}+x^{6}+x^{8}+.... \right )\left ( 1+x^{4}+x^{8}+x^{12}+.... \right )\left ( 1+x^{6}+x^{12}+x^{18}+.... \right )$ Ans. $\frac{1}{\left ( 1-x^ ... \right )\left ( 1-x^{6} \right )}$........now not able to proceed. 2.Provide a closed formula for the sequence it determines x2+3x+7+(1/(1-x2))

asked May 18 in Combinatory by mbisht (161 points) | 144 views

0 votes

2 answers

14

Generating Function
Find $\left [ x^{50} \right ]$ $\left ( x^{6}+x^{7}+x^{8}+.... \right )^{6}$

asked May 18 in Combinatory by Nils Junior (881 points) | 68 views

0 votes

1 answer

15

Generating function
1. Find a closed form for the generating function for the sequence $1,1,0,1,1,1,1,1,1,1,...........$ 2. Find a closed form for the generating function for the sequence $a_n= 2n+3$ for all $n=0,1,2,....$

asked May 17 in Combinatory by mbisht (161 points) | 48 views

0 votes

1 answer

16

kenneth rosen chapter 5 exercise 5.5 ques 51

asked May 17 in Combinatory by mbisht (161 points) | 78 views

0 votes

0 answers

17

ISI 2018 MMA 1
The number of common terms in the two sequence (3,7,11,...,407} and {2,9,16,...,70} is A)13 B)14 C)15 D)16 [closed]

asked May 14 in Combinatory by Tesla! Boss (16.1k points) | 51 views

0 votes

2 answers

18

combinatorics
There were 4 blue french horns, 5 yellow Umbrellas and 6 Suits in a shop. Ted, Barney, Lily, Marshal and Robin came to the shop to buy the items. How many different results could have been recorded if all of the items were sold?

asked May 5 in Combinatory by gow tham (39 points) | 70 views

0 votes

2 answers

19

ISI 2014 PCB A2
Let m and n be two integers such that m ≥ n ≥ 1. Count the number of functions f : {1, 2, · · · , n} → {1, 2, · · · , m} of the following two types: (a) strictly increasing; i.e., whenever x < y, f(x) < f(y), and (b) non-decreasing; i.e., whenever x < y, f(x) ≤ f(y).

asked May 1 in Combinatory by tathatj (67 points) | 84 views

+3 votes

1 answer

20

Discrete Maths Kenneth Rosen chapter 6.3 Question 24

asked Apr 30 in Combinatory by surajumang08 (189 points) | 84 views

+1 vote

1 answer

21

ISI 2017 PCB A2
Let $a,b,c$ and $d$ be real number such that $a+b=c+d$ and $ab=cd$. Prove that $a^{n}+b^{n}=c^{n}+d^{n}$ for all positive integer $n$.

asked Apr 28 in Combinatory by Tesla! Boss (16.1k points) | 103 views

+1 vote

2 answers

22

ISI2017-MMA-22
The five vowels—$A, E, I, O, U$—along with $15$ $X’s$ are to be arranged in a row such that no $X$ is at an extreme position. Also, between any two vowels, there must be at least $3$ $X’s$. The number of ways in which this can be done is $1200$ $1800$ $2400$ $3000$

asked Apr 25 in Combinatory by Tuhin Dutta Loyal (7.9k points) | 136 views

0 votes

0 answers

23

#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 Apr 17 in Combinatory by Abhinavg (259 points) | 49 views

0 votes

2 answers

24

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 Apr 15 in Combinatory by Sachin Kumar Verma (49 points) | 85 views

0 votes

0 answers

25

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 Apr 15 in Combinatory by Mk Utkarsh Boss (12.6k points) | 74 views

0 votes

1 answer

26

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 Apr 14 in Combinatory by Kushagra Chatterjee Loyal (8.2k points) | 70 views

0 votes

0 answers

27

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 (611 points) | 58 views

+1 vote

1 answer

28

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 (611 points) | 73 views

+1 vote

0 answers

29

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 (1.4k points) | 117 views

0 votes

1 answer

30

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

asked Apr 12 in Combinatory by Abhinavg (259 points) | 126 views

tags	tag:apple
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

Recent questions in Combinatory

Recent Posts

Recent Blog Comments