Recent questions and answers in Combinatory

0 votes

1 answer

1

Stuck on this combinatorics question
A florist sells roses of five different colors. How many bunches of a half-dozen roses can be formed? a 196 210 236 300 Please help me understand this question with proper explanation. I got the answer but looking for the logical reasoning to it.

answered 7 minutes ago in Combinatory by Mk Utkarsh Boss (30k points) | 7 views

0 votes

0 answers

2

How this can be done.
Find the number of ways 4 fruits can be chosen out of 8 fruits so as to exclude the largest fruit.

asked 22 hours ago in Combinatory by `JEET Active (2.3k points) | 25 views

0 votes

0 answers

3

How to do such questions
Find the largest integer value of x satisfying the inequality ${10 \choose x-1}$ < 2${10 \choose x}$

asked 23 hours ago in Combinatory by `JEET Active (2.3k points) | 24 views

+1 vote

0 answers

4

How to do this question
Compute the coefficient value of $ x^3 y^2z$ in the $(x-y+3z)^6$

asked 23 hours ago in Combinatory by `JEET Active (2.3k points) | 42 views

0 votes

0 answers

5

Combinatorics
A ball is dropped from a height of 15 feet. Each time it strikes the pavement after falling from a height of h feet, it rebounds to a height of 0.6 h feet. What is the total distance the ball travels up and down? Please confirm the answer

asked 1 day ago in Combinatory by `JEET Active (2.3k points) | 37 views

0 votes

0 answers

6

ME TEST 1

asked 1 day ago in Combinatory by himgta Active (2.9k points) | 16 views

0 votes

2 answers

7

Rosen-Recurrence Relation
Find a recurrence relation for the number of bit strings of length n that contains a pair of consecutive 0s

answered 3 days ago in Combinatory by Tejasvi96 (243 points) | 25 views

+1 vote

0 answers

8

Madeeasy test series full syllbus
Let M(x) = $\frac{x^{2018}}{(1-x)^{2019}}$ we define M(x) = $ \sum_{r=0}^{infinity}a_{r}x^{r}$ . then $a_{r}$ is equal to- option are –

asked 3 days ago in Combinatory by register_user_19 Active (1.2k points) | 20 views

+14 votes

4 answers

9

GATE2000-1.1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is $3$ $8$ $9$ $12$

answered 4 days ago in Combinatory by Suneel Padala (215 points) | 2.4k views

0 votes

0 answers

10

#Combinations
Number of ways of splitting 10 people into 2 teams of 6 and 4 people respectively. Answer- $^{10}c_{6}$ Number of ways of splitting 10 people into 2 teams of 5 people each. Answer – $^{10}c_{5} /2$ Please explain why we divide by 2?

asked 4 days ago in Combinatory by Nymeria (429 points) | 26 views

+1 vote

1 answer

11

AAI JE (IT) 2019 Q-30
Can someone solve this and tell how it’s 160.

answered 6 days ago in Combinatory by Hemanth_13 Loyal (5.4k points) | 50 views

+10 votes

8 answers

12

GATE2018-1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$

answered 6 days ago in Combinatory by Prateek K Active (1.6k points) | 3.4k views

+1 vote

0 answers

13

#discrete matmatics
recurrence relation 2a$_{n}=a_{n-1}+2^{n}$ intial condtion a$_{0}$=1 value of a$_{100}$

asked 6 days ago in Combinatory by amit166 Junior (529 points) | 25 views

+1 vote

1 answer

14

ME Test Series

answered Dec 11 in Combinatory by Lakshman Patel RJIT Boss (20.9k points) | 46 views

+1 vote

0 answers

15

number system
what is the meaning of two consecutive 1’s in a string? suppose for the string 011 here whether two consecutive 1’s present or not ….

asked Dec 10 in Combinatory by utpal podder (295 points) | 23 views

–1 vote

2 answers

16

Aai it 2018

answered Dec 10 in Combinatory by Satbir Active (1.2k points) | 98 views

0 votes

0 answers

17

Rosen
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

asked Dec 10 in Combinatory by aditi19 Active (2.2k points) | 16 views

+1 vote

1 answer

18

#tifr 2019
if $m$ and $n$ are postive integer then $2^{n}-1$ is prime if n is prime $m^{n-1}=1 mod n$ which is true

answered Dec 10 in Combinatory by Lakshman Patel RJIT Boss (20.9k points) | 135 views

0 votes

0 answers

19

Self Doubt
Given a standard 9*9 sudoku, What is the probability that I solved a sudoku and it results into a diagonal sudoku ? ( 1. Is it a valid question ? 2. What would be the difficulty ? )

asked Dec 10 in Combinatory by HeadShot Active (3.7k points) | 13 views

0 votes

0 answers

20

SELF DOUBT GENERATING FUNCTION
Difference between getting closed form of generating function and closed form of the given sequence ,pls someone explain with an example

asked Dec 10 in Combinatory by codingo1234 (477 points) | 20 views

+2 votes

3 answers

21

TIFR 2019
There are 10 houses in a row. Each house can be colored in one of three - blue or red or green. If you color a house with blue or red then you have to color green in the exact right one of that house. How many different ways all 10 houses can be colored?

answered Dec 9 in Combinatory by arvin Boss (10.2k points) | 312 views

+27 votes

5 answers

22

GATE2004-75
Mala has the colouring book in which each English letter is drawn two times. She wants to paint each of these $52$ prints with one of $k$ colours, such that the colour pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $k$ that satisfies this requirement? $9$ $8$ $7$ $6$

answered Dec 7 in Combinatory by chauhansunil20th Active (2k points) | 2.7k views

+13 votes

3 answers

23

GATE1999-2.2
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves? $1638$ $2100$ $2640$ None of the above

answered Dec 7 in Combinatory by chauhansunil20th Active (2k points) | 2.9k views

0 votes

0 answers

24

DM: K Rosen: Countings
Question: A group contains 4 men and 4 women. How many ways are there to arrange these people in a row if the men ad women alternate. Method 1: row can be started either with woman or a man. $mwmwmwmw$ or $wmwmwmwm$ And further we can permute men and ... select the places for men and further we can permute man and women So answer should be 5*4!*4! ways. which one is correct?

asked Dec 4 in Combinatory by chauhansunil20th Active (2k points) | 28 views

0 votes

1 answer

25

GENERATING FUNCTIONS

answered Dec 4 in Combinatory by Ayush Upadhyaya Boss (19.3k points) | 88 views

0 votes

0 answers

26

Kenneth_Rosen_GF
Find a closed form for the exponential generating function for the sequence $\{a_n\}$ where $a_n=\frac{1}{(n+1)(n+2)}$ I broke it down into partial fractions and got $a_n=\frac{1}{n+1}-\frac{1}{n+2}$ ... $\sum_{n=0}^{\infty}\frac{1}{(n+2)}.\frac{x^n}{n!}$

asked Dec 4 in Combinatory by Ayush Upadhyaya Boss (19.3k points) | 40 views

+2 votes

0 answers

27

Kenneth Rosen
Use Generating function to determine,the number of different ways $10$ identical balloons can be given to four children if each child receives atleast $2$ ballons? Ans given $(x^{2}+x^{3}+.........................)^{4}$ But as there is a upper bound I think answer will be $(x^{2}+x^{3}+.........................+{\color{Red} {x^{10}}})^{4}$ Which one is correct? plz confirm

asked Dec 4 in Combinatory by srestha Veteran (104k points) | 128 views

0 votes

3 answers

28

Generating Function
What will be solution of this function for coefficient of $x^{100}$? $\frac{1}{\left ( 1-x^{10} \right )(1-x^{20})(1-x^{50})}$

answered Dec 4 in Combinatory by sudoankit Active (1.8k points) | 141 views

0 votes

0 answers

29

Generating function(Find Coefficient of x^100) [closed]

asked Dec 3 in Combinatory by !KARAN Junior (923 points) | 63 views

0 votes

0 answers

30

Generating Function (Kenneth Rosen)
Ques #29 from Generating function Use generating functions to find the number of ways to make change for $\$100$ using a) $\$10$, $\$20$, and $\$50$ bills. b) $\$5$, $\$10$, $\$20$, and $\$50$ bills. c) $\$5$, $\$10$, $\$ ... $5$, $\$10$ and $\$20$, bills if at least one and no more than four of each denomination is used.

asked Dec 2 in Combinatory by !KARAN Junior (923 points) | 41 views

0 votes

1 answer

31

Counting MadeEasy

answered Dec 2 in Combinatory by Mk Utkarsh Boss (30k points) | 52 views

0 votes

1 answer

32

GATEBOOK-2019-DM2-2
In how many ways can $2$ RED and $4$ BLUE ROOKS be placed on an $8-by-8$ board so that no two ROOKS can attack one another? $8! \times 8!$ $8! \times \frac{8!}{2!4!}$ $8! \times \frac{8!}{2!4!2!}$ ${}^8P_4$

answered Dec 2 in Combinatory by kumar.dilip Active (3.3k points) | 67 views

+11 votes

4 answers

33

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 Nov 30 in Combinatory by sidlewis (493 points) | 1.6k views

0 votes

0 answers

34

ACE Testseries

asked Nov 30 in Combinatory by Vipin Rai (391 points) | 39 views

+1 vote

1 answer

35

GATEBOOK-2019-DM2-20
How many ways a set of $5$ elements can be divided into two unordered partitions where each partition gets at least one element?

answered Nov 29 in Combinatory by Mk Utkarsh Boss (30k points) | 83 views

0 votes

1 answer

36

GATEBOOK-2019-DM2-12
How many even integers $≥ 4000$ and $< 7000$ have four different digits? $128$ $728$ $328$ $528$

answered Nov 29 in Combinatory by Mk Utkarsh Boss (30k points) | 48 views

0 votes

0 answers

37

Ace test series
A medical student has to work in a hospital for five days in january.However,he is not allowed to work two consecutive days in the hospital.in how many different ways can he choose the five days he will work in the hospital? A)C(27,5) B)C(26,5) C)C(27,4) D)C(26,4)

asked Nov 26 in Combinatory by talha hashim Active (4.5k points) | 52 views

0 votes

0 answers

38

ace academy test series
Please explain in some detail.

asked Nov 23 in Combinatory by amitqy Junior (957 points) | 19 views

0 votes

0 answers

39

in how many ways 4 different balls can be placed in 5 different boxes so that no box contains all 4 balls

asked Nov 23 in Combinatory by Sanjay Sharma Veteran (50k points) | 33 views

0 votes

0 answers

40

self Doubt
$\frac{1}{2}\sum_{p=0}^{k-1} (p^2 + 3p+2).2^p$ where n = 2k. Solve the summation

asked Nov 23 in Combinatory by Shaik Masthan Boss (43.2k points) | 59 views

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