Recent questions and answers in Combinatory

+1 vote

1 answer

1

Pgee 2013
You have a box containing 10 black and 10 blue socks.What is the minimum number of times you need to pull out so that you have a pair of the same color?

answered 15 hours ago in Combinatory by Manas Mishra Active (2.8k points) | 19 views

0 votes

0 answers

2

Kenneth H Rosen 7th edition
Please see example 6. l am not getting the mathematical insight. Can anyone please tell how they are arriving at the answer.

asked 1 day ago in Combinatory by Psnjit (207 points) | 21 views

+2 votes

1 answer

3

Rosen 7e Exercise-6.5 question 45.b page 433
How many ways can n books be placed on k distinguishable shelves if no two books are the same, and the positions of the books on the shelves matter?

answered 2 days ago in Combinatory by ma1999 (11 points) | 131 views

0 votes

1 answer

4

Madeeasy Discrete Maths notes
How many 5 letter word possible having atleast 2 a's ?

answered Apr 9 in Combinatory by tusharp Loyal (6.4k points) | 52 views

0 votes

1 answer

5

Self doubt
How is the problem.. Distribute 5 toys such that each of 3 child get atleast 1 Different from sum of 3 no. X+y+z=5 such that each digit >= 1. Plz explain ?

answered Apr 4 in Combinatory by hitendra singh Active (1.8k points) | 53 views

0 votes

0 answers

6

Combinatorics
There are 6n flowers of one type and 3 flowers of second type, total no. Of garlands possible?

asked Apr 2 in Combinatory by Manoj Kumar Pandey (177 points) | 12 views

0 votes

0 answers

7

General Query: Self doubt(Math+Automata)
Can somebody explain What is identity permutation?

asked Apr 1 in Combinatory by srestha Veteran (111k points) | 21 views

0 votes

0 answers

8

website
There is 4 coins 1 paisa, 5 paise, 10 paise, 25 paise using these coins we have to make 50 paisa how many combination can we make ?

asked Mar 31 in Combinatory by Cristine Active (1.6k points) | 22 views

+1 vote

3 answers

9

MadeEasy Subject Test 2019: Combinatory - Permutations And Combinations
Q.The number of ways, we can arrange 5 books in 3 shelves ________.

answered Mar 26 in Combinatory by Arkaprava (45 points) | 347 views

+2 votes

2 answers

10

GATE2019-5
Let $U = \{1, 2, \dots , n\}$ Let $A=\{(x, X) \mid x \in X, X \subseteq U \}$. Consider the following two statements on $\mid A \mid$. $\mid A \mid = n2^{n-1}$ $\mid A \mid = \Sigma_{k=1}^n k \begin{pmatrix} n \\ k \end{pmatrix}$ Which of the above statements is/are TRUE? Only I Only II Both I and II Neither I nor II

answered Mar 25 in Combinatory by KINGSLAYER (65 points) | 2.2k views

0 votes

0 answers

11

Allen Career Institute: Discrete Mathematics
A certain software was being tested by using error seeding strategy in which $22$ errors were seeded. $14$ of seeded errors were detected apart from $140$ unseeded errors when the code was tested using the complete test suit. Calculate the estimated no. of undetected errors in the code after complete testing _____

asked Mar 22 in Combinatory by srestha Veteran (111k points) | 26 views

0 votes

1 answer

12

MadeEasy Full Length Test 2019: Combinatory - Permutations And Combinations
The number of ways 5 letter be put in 3 letter boxes A,B,C. If letter box A must contain at least 2 letters.

answered Mar 19 in Combinatory by vizzard110 (11 points) | 149 views

+1 vote

1 answer

13

Model Question IISc CDS CS Written Test Sample question
Anand is preparing a pizza with 8 slices, and he has 10 toppings to put on the pizza. He can put only one topping on each slice but can use the same topping on zero or more slices. In how many unique ways can he prepare the slices so that the same topping is not used in adjacent slices?

answered Mar 15 in Combinatory by Arkaprava (45 points) | 125 views

+10 votes

5 answers

14

TIFR2015-A-7
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \times 8$ chessboard? $64$ $65$ $204$ $144$ $256$

answered Mar 15 in Combinatory by Debargha Bhattacharj (215 points) | 621 views

+13 votes

5 answers

15

GATE2003-34
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ ... $\left( \begin{array}{c} m - kn + n + k - 2 \\ n - k \end{array} \right)$

answered Mar 9 in Combinatory by Debargha Bhattacharj (215 points) | 2k views

+17 votes

3 answers

16

GATE2002-13
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$ the number of ways is $2$, i.e., $1+2, 2+1$. Give only the answer ... integer $n \geq k$ be expressed as the sum of $k$ positive integers (which are not necessarily distinct). Give only the answer without explanation.

answered Mar 9 in Combinatory by Debargha Bhattacharj (215 points) | 990 views

+2 votes

1 answer

17

Rosen 7e, Advance Counting techniques , Question 6.f
Find the generating function for the sequence $\left \{ a_n \right \} where $ $a_n = \Large \binom{10}{n+1} $ ... $\Large \color{red}{ \frac{( 1+x )^{10} - 1}{x} }$ Please verify

answered Mar 9 in Combinatory by Debdeep1998 Junior (635 points) | 41 views

0 votes

1 answer

18

ACE Test Series: Generating Function
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$ where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}$ is $a)3\left ( 1+3x \right )^{-2}$ $b)3\left ( 1-3x \right )^{-2}$ $c)2\left ( 1+3x \right )^{-3}$ $d)2\left ( 1-3x \right )^{-3}$

answered Mar 9 in Combinatory by ankitgupta.1729 Boss (10.7k points) | 57 views

0 votes

1 answer

19

Kenneth Rosen Edition 6th Exercise 6.1 Example 7 (Page No. 399)
this is an example taken from Rosen. but I’m unable to understand to understand the solution given there can someone pls explain me in details

answered Mar 4 in Combinatory by Gawade Sahadev (291 points) | 50 views

+8 votes

7 answers

20

Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?

answered Mar 3 in Combinatory by srestha Veteran (111k points) | 2k views

0 votes

1 answer

21

Rosen Ex.6.1
Find a recurrence relation for the number of ways to lay out a walkway with slate tiles if the tiles are red, green, or gray so that no two red tiles are adjacent and tiles of the same color are considered indistinguishable

answered Mar 3 in Combinatory by vipul2097 (165 points) | 31 views

0 votes

1 answer

22

#Combinatorics

answered Mar 1 in Combinatory by Satbir Loyal (5.9k points) | 100 views

0 votes

0 answers

23

Pg 345 Question 23, 6th Edition KH Rosen
How many strings of three decimal digits do not contain the same digit three times? have exactly two digits that are 4s? I know question is easy but the answer is not matching with the one given over here Please someone verify.. Does the word “string” mean that we can take 0 as the first digit as well? [closed]

asked Feb 27 in Combinatory by MiNiPanda Boss (21.9k points) | 41 views

0 votes

2 answers

24

Kenneth Rosen Example 9 Ch.5.2
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 ... 't understand this part. How is it concluded that remaining nine servers are insufficient when at most 59 connections are used?

answered Feb 25 in Combinatory by Satbir Loyal (5.9k points) | 70 views

0 votes

2 answers

25

Kenneth Rosen Edition 6th Exercise 5.2 Example 9 (Page No. 350)
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 ... of direct connections needed to achieve this goal? Please Explain in this question how pigeonhole principle is applied .

answered Feb 24 in Combinatory by Satbir Loyal (5.9k points) | 134 views

+1 vote

1 answer

26

Rosen example 12 Ch 5.2
Show that every sequence of $n^2$+1 distinct real numbers contains a subsequence of length n+1 that is either strictly increasing or strictly decreasing.

answered Feb 24 in Combinatory by Shaik Masthan Veteran (60.2k points) | 49 views

+17 votes

3 answers

27

GATE2000-5
A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it, counting repetitions. What is the number of multisets of size $4$ that can be constructed from n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?

answered Feb 19 in Combinatory by Priyadrasta Raut (373 points) | 1.2k views

+1 vote

2 answers

28

Permutations combination
A playoff between two teams consists of atmost five games.The first team that wins three games wins the playoff.In how many different ways can the playoff occur?

answered Feb 16 by subhrob (373 points) | 480 views

+6 votes

4 answers

29

TIFR2018-A-6
What is the minimum number of students needed in a class to guarantee that there are at least $6$ students whose birthdays fall in the same month ? $6$ $23$ $61$ $72$ $91$

answered Feb 10 in Combinatory by Satbir Loyal (5.9k points) | 317 views

+17 votes

2 answers

30

TIFR2014-A-5
The rules for the University of Bombay five-a-side cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students? $23$ $91$ $60$ $49$ None of the above.

answered Feb 10 in Combinatory by Satbir Loyal (5.9k points) | 791 views

+15 votes

6 answers

31

TIFR2016-A-15
In a tournament with $7$ teams, each team plays one match with every other team. For each match, the team earns two points if it wins, one point if it ties, and no points if it loses. At the end of all matches, the teams are ordered in the descending order of their ... total number of points a team must earn in order to be guaranteed a place in the next round? $13$ $12$ $11$ $10$ $9$

answered Feb 10 in Combinatory by Satbir Loyal (5.9k points) | 598 views

+22 votes

6 answers

32

GATE2004-IT-35
In how many ways can we distribute $5$ distinct balls, $B_1, B_2, \ldots, B_5$ in $5$ distinct cells, $C_1, C_2, \ldots, C_5$ such that Ball $B_i$ is not in cell $C_i$, $\forall i= 1,2,\ldots 5$ and each cell contains exactly one ball? $44$ $96$ $120$ $3125$

answered Feb 9 in Combinatory by Satbir Loyal (5.9k points) | 2.4k views

+13 votes

3 answers

33

CMI2010-A-02
We need to choose a team of $11$ from a pool of $15$ players and also select a captain. The number of different ways this can be done is $ \begin{pmatrix} 15 \\ 11 \end{pmatrix}$ $11$ . $ \begin{pmatrix} 15 \\ 11 \end{pmatrix}$ $15 . 14 . 13 . 12 . 11 .10 . 9 . 8 . 7 . 6 . 5$ $(15 . 14 . 13 . 12 . 11 .10 . 9 . 8 . 7 . 6 . 5) . 11$

answered Feb 9 in Combinatory by Satbir Loyal (5.9k points) | 599 views

0 votes

1 answer

34

Self Doubt
From a group of 5 woman and 7 man we have to select a committee consisting of 2 woman and 3 men. Find the total number of ways to select such committed if (1 and 2 are a separate question) 1. Four man refuse to be in the same committee 2. 2 woman refuse to be in the same committee.

answered Feb 8 in Combinatory by sai charan chakrala (285 points) | 66 views

+35 votes

8 answers

35

GATE2016-1-27
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 Feb 1 in Combinatory by Sambhrant Maurya Active (1.7k points) | 6.8k views

0 votes

1 answer

36

generating function

answered Feb 1 in Combinatory by sgrpwr (15 points) | 77 views

+1 vote

1 answer

37

Letters in boxes - combinations
Q .) The number of ways can 5 letter be put in 3 boxes A, B,C such that A has at least 2 letters. My approach: Number of ways to choose 2 letters out of 5 is 5C2. And for each such combination the remaining 3 letter have 3 choice. Therefore 5C2 * 3^3, but this is incorrect. Please point out the fault in my understanding and also the correct way to solve it

answered Jan 31 in Combinatory by balchandar reddy san Active (2.9k points) | 51 views

0 votes

0 answers

38

Arrangement
Number of ways we can arrange 5 books in 3 selves___________ [closed]

asked Jan 31 in Combinatory by srestha Veteran (111k points) | 87 views

0 votes

0 answers

39

The number of ways in which we can place 3 white pawns and 3 black pawns on a 3 . 3 Chessboard is equal to [closed]

asked Jan 30 in Combinatory by mehul vaidya Active (4.3k points) | 26 views

0 votes

2 answers

40

MadeEasy Test Series
What is the number of seven digit integers possible with sum of the digits equal to 11 and formed by using the digits 1, 2 and 3 only?

answered Jan 29 in Combinatory by Shaik Masthan Veteran (60.2k points) | 84 views

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