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Recent questions and answers in Combinatory
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Kenneth Rosen Edition 7 Exercise 6.1 Question 57 (Page No. 398)
The name of a variable in the JAVA programming language is a string of between $1$ and $65,535$ characters, inclusive, where each character can be an uppercase or a lowercase letter, a dollar sign, an underscore, or a digit, except that the first character must not be a digit. Determine the number of different variable names in JAVA.
Shriram BM
answered
in
Combinatory
Mar 4
by
Shriram BM
1.1k
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kenneth-rosen
discrete-mathematics
counting
descriptive
7
votes
4
answers
2
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
Priyam Garg
answered
in
Combinatory
Feb 28
by
Priyam Garg
7.7k
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gatecse-2023
combinatory
recurrence-relation
1-mark
19
votes
18
answers
3
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
ravi2002
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in
Combinatory
Feb 26
by
ravi2002
17.9k
views
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
2
votes
4
answers
4
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 $a)3\left ( 1+3x \right )^{-2}$ $b)3\left ( 1-3x \right )^{-2}$ $c)2\left ( 1+3x \right )^{-3}$ $d)2\left ( 1-3x \right )^{-3}$
Priyam Garg
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in
Combinatory
Feb 20
by
Priyam Garg
1.5k
views
generating-functions
discrete-mathematics
24
votes
6
answers
5
TIFR CSE 2012 | Part A | Question: 7
It is required to divide the $2n$ members of a club into $n$ disjoint teams of $2$ members each. The teams are not labelled. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^n . n!}$ $\frac{n!}{2}$ None of the above
Priyam Garg
answered
in
Combinatory
Feb 18
by
Priyam Garg
4.5k
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tifr2012
combinatory
balls-in-bins
0
votes
2
answers
6
Kenneth Rosen Edition 7 Exercise 6.3 Question 26 (Page No. 414)
Thirteen people on a softball team show up for a game. How many ways are there to choose $10$ players to take the field? How many ways are there to assign the $10$ positions by selecting players from the $13$ people who show ... ways are there to choose $10$ players to take the field if at least one of these players must be a woman?
Priyam Garg
answered
in
Combinatory
Feb 11
by
Priyam Garg
4.4k
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
0
votes
0
answers
7
Combinatorics & Probability
A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyone except the individual who just called. (a) By how many different paths can a rumor ... in $N$ calls? (c) What is the probability that if $A$ starts the rumor, then $A$ receives the third calls?
Debargha Mitra Roy
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in
Combinatory
Feb 8
by
Debargha Mitra Roy
126
views
combinatory
counting
6
votes
2
answers
8
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 56
The coefficient of $x^6$ in the expansion of $A(x)$ is, where $ A(x)=\frac{x(1+x)}{(1-x)^3} $
squirrel69
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in
Combinatory
Feb 6
by
squirrel69
484
views
goclasses2024-mockgate-14
numerical-answers
combinatory
recurrence-relation
2-marks
0
votes
1
answer
9
#self doubt
Can someone please explain the following case of combination I means identical D means different DOIB with boxes being empty and non empty As in this question the given value in question itself i am not able to interpret. https://gateoverflow.in/420251/go-classes-test-series-2024-mock-gate-test-12-question-17
GauravRajpurohit
answered
in
Combinatory
Jan 31
by
GauravRajpurohit
180
views
discrete-mathematics
4
votes
1
answer
10
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 30
A university's mathematics department has $10$ professors and will offer $20$ different courses next semester. Each professor will be assigned to teach exactly $2$ of the courses, and each course will have exactly one professor assigned to teach it. If any professor ... $10^{20}-2^{10}$ $\dfrac{20 ! 10 !}{2^{10}}$
SankarVinayak
answered
in
Combinatory
Jan 29
by
SankarVinayak
473
views
goclasses2024-mockgate-13
goclasses
combinatory
counting
1-mark
0
votes
4
answers
11
Computer Science - UGC NET 2021 [ Question ID = 2353 ]
How many ways are there to assign 5 different jobs to 4 different employees if every employee is assigned at least 1 job ? 1024 625 240 20
swapnil8222
answered
in
Combinatory
Jan 25
by
swapnil8222
661
views
discrete-mathematics
permutation-combination
engineering-mathematics
6
votes
2
answers
12
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 17
The number of ways that one can divide $10$ distinguishable objects into $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the piles are also distinguishable?
krishnajsw
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in
Combinatory
Jan 21
by
krishnajsw
837
views
goclasses2024-mockgate-12
goclasses
numerical-answers
combinatory
counting
1-mark
5
votes
2
answers
13
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 18
The number of ways that one can divide $10$ distinguishable objects in $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the objects are also indistinguishable?
GauravRajpurohit
answered
in
Combinatory
Jan 21
by
GauravRajpurohit
811
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goclasses2024-mockgate-12
goclasses
numerical-answers
combinatory
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1-mark
1
vote
1
answer
14
selfdoubt combinatory
In how many ways can you distribute 4 different choclates to 3 people such that each gets atleast 1 choclate.
swapnil8222
answered
in
Combinatory
Jan 14
by
swapnil8222
168
views
self-doubt
made-easy-test-series
7
votes
2
answers
15
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 44
Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the last character must be a digit, and any character that is a sign must be followed by a digit. There ... by $N_k=a N _{k-1}+b N _{k-2}$, for $k \geq 3$. What is $a+ b?$
Sujith48
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in
Combinatory
Jan 14
by
Sujith48
514
views
goclasses2024-mockgate-11
goclasses
numerical-answers
combinatory
recurrence-relation
2-marks
38
votes
7
answers
16
GATE CSE 1999 | Question: 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
yuyutsu
answered
in
Combinatory
Jan 10
by
yuyutsu
12.0k
views
gate1999
combinatory
normal
34
votes
8
answers
17
GATE CSE 2002 | Question: 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 ... $n \geq k$ be expressed as the sum of $k$ positive integers (which are not necessarily distinct). Give only the answer without explanation.
GauravRajpurohit
answered
in
Combinatory
Dec 26, 2023
by
GauravRajpurohit
7.1k
views
gatecse-2002
combinatory
normal
descriptive
balls-in-bins
0
votes
1
answer
18
Kenneth Rosen Edition 7 Exercise 8.2 Question 48 (Page No. 526)
Some linear recurrence relations that do not have constant coefficients can be systematically solved. This is the case for recurrence relations of the form $f (n)a_{n} = g(n)a_{n-1} + h(n).$ Exercises $48-50$ ...
cc_flow
answered
in
Combinatory
Dec 25, 2023
by
cc_flow
390
views
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
33
votes
6
answers
19
GATE CSE 2000 | Question: 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 ... n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?
This_is_Nimishka
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in
Combinatory
Dec 14, 2023
by
This_is_Nimishka
7.7k
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gatecse-2000
combinatory
normal
descriptive
0
votes
1
answer
20
Self Doubt on Combinatory Discrete Mathematics
Given there are 3 full baskets of apples, mangoes, and oranges. How many ways possible if a) You need to buy any 4 fruits out of these 3 baskets ? b) you buy any 4 fruits such that you take at least one from each basket ?
Negan
answered
in
Combinatory
Dec 3, 2023
by
Negan
221
views
discrete-mathematics
combinatory
0
votes
1
answer
21
#self doubt
The number of bit strings of length 8 that will either start with 1 or end with 00 is? (https://gateoverflow.in/15898/isro2014-19) In the ‘either or’ case we will include the ‘and’ case also? means: 1 string starting with 1 2 stating ending with 00 3 strings start with 1 and end with 00 all above cases will be included in either or case or only 1,2 will be included?
yahba
answered
in
Combinatory
Nov 20, 2023
by
yahba
191
views
combinatory
0
votes
0
answers
22
how many it string of length 10 over the alphabet {a,b,c} have either exactly three a's or exactly four b's
_shreya123
asked
in
Combinatory
Nov 18, 2023
by
_shreya123
219
views
combinatory
strings
14
votes
3
answers
23
GATE CSE 2023 | Question: 38
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|=|B|=k$ and $A \cap B=\emptyset$. We say that a permutation of $U$ separates $A$ from $B$ if ... $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^{2}$
ssingla
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in
Combinatory
Nov 9, 2023
by
ssingla
6.2k
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gatecse-2023
combinatory
counting
2-marks
0
votes
1
answer
24
Kenneth Rosen Edition 7 Exercise 6.5 Question 40 (Page No. 433)
How many ways are there to travel in $xyzw$ space from the origin $(0, 0, 0, 0)$ to the point $(4, 3, 5, 4)$ by taking steps one unit in the positive $x,$ positive $y,$ positive $z,$ or positive $w$ direction?
Vandana04
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in
Combinatory
Oct 23, 2023
by
Vandana04
282
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
2
votes
4
answers
25
Permutation and Combination
In how many ways can 3 non-negative integers be chosen such that a + b + c = 10 where a >= -1 , b >= -5 and c >= 3 ? 36 66 105 None
Zuleen Khan
answered
in
Combinatory
Oct 22, 2023
by
Zuleen Khan
446
views
combinatory
discrete-mathematics
0
votes
1
answer
26
Combinatorics, Discrete Maths (self doubts)
Consider the set of 4 -digit positive integers. How many of them have their digits in :- a) strictly decreasing order ? b) non decreasing order ? c) non increasing order ?
Abhay123
answered
in
Combinatory
Oct 20, 2023
by
Abhay123
375
views
combinatory
sorting
discrete-mathematics
goclasses
25
votes
6
answers
27
GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
akshay_123
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in
Combinatory
Oct 4, 2023
by
akshay_123
11.7k
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gatecse-2021-set2
combinatory
counting
numerical-answers
2-marks
0
votes
1
answer
28
Kenneth Rosen Edition 7 Exercise 6.3 Question 39 (Page No. 415)
How many license plates consisting of three letters followed by three digits contain no letter or digit twice?
Vijay111
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in
Combinatory
Oct 2, 2023
by
Vijay111
293
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kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
0
votes
1
answer
29
Kenneth Rosen Edition 7 Exercise 6.3 Question 38 (Page No. 414)
How many ways are there to select $12$ countries in the United Nations to serve on a council if $3$ are selected from a block of $45, 4$ are selected from a block of $57,$ and the others are selected from the remaining $69$ countries?
Vijay111
answered
in
Combinatory
Oct 2, 2023
by
Vijay111
603
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
17
votes
8
answers
30
GATE CSE 2008 | Question: 24
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then $P = Q - k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
ssingla
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in
Combinatory
Sep 24, 2023
by
ssingla
4.8k
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2
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31
GoClasses Youtube
Determine the Number of $6$ digit integers (no leading zeroes) in which no digit is repeated and its divisible by $4$.
Swarnava Bose
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in
Combinatory
Aug 16, 2023
by
Swarnava Bose
429
views
discrete-mathematics
permutation-combination
combinatory
3
votes
1
answer
32
Combinatorics Question uOttawa (University of Ottawa)
Consider the fourteen letters: $\text{A A A B B C C C C C D E E E}$ . An ARRANGEMENT is a sequence using $\text{all}$ ... order, somewhere in the arrangement). c) How many words have all letters distinct? d) How many arrangements have no two vowels consecutive?
Deepak Poonia
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in
Combinatory
Jul 1, 2023
by
Deepak Poonia
623
views
combinatory
discrete-mathematics
0
votes
1
answer
33
Byjus Workbook
Sir I am getting answer as 25 my approach k+1=3 k=2 n=12 nk+1=25 @sachinmittal1 @gate_cse
JayRathi
asked
in
Combinatory
Jun 14, 2023
by
JayRathi
371
views
0
votes
0
answers
34
Self doubt on Combinatorics Discrete Mathematics
What is the total number of integer partitions ( unordered Summation) of the natural number 8 ? I am getting 22. Is it correct ?
Swarnava Bose
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in
Combinatory
Jun 9, 2023
by
Swarnava Bose
209
views
combinatory
discrete-mathematics
0
votes
1
answer
35
self doubt on Combinatory Discrete Mathematics
A power series expression has been converted to Partial Fractions to get :- $\frac{3}{1+5x} - \frac{2}{7-2x}+ \frac{5x}{3+2x} + \frac{7x}{5-2x}$ Find the Coefficient of $x^{n}$ where n represents natural number.
Swarnava Bose
asked
in
Combinatory
Jun 3, 2023
by
Swarnava Bose
391
views
combinatory
discrete-mathematics
0
votes
0
answers
36
Let (1 + x)n = C0 + C1x + C2x2 + . . . + Cnxn, n being a positive integer. Then find the value of ( 1 + C0 C1 ) ( 1 + C1 C2 ) . . . ( 1 + Cn−1 Cn
JISAANNAGEORGE
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in
Combinatory
May 11, 2023
by
JISAANNAGEORGE
276
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combinatory
0
votes
0
answers
37
Clrs ex 5.2-2 chapter5 page133 4thedition
Hiring assistant. Initially assistant is NULL We have n candidates who hv come to interview for the position of assistant. Each candidate has distinct scores or level of qualifications. Now initially we have no assistant(stated earlier), so the first ... to solve this sum, and my answer is The best candidate comes in at kth position. Am I right? Thankyou.
yuyutsu
asked
in
Combinatory
May 2, 2023
by
yuyutsu
194
views
0
votes
1
answer
38
Flamingos Fanny and Freddy have three offspring: Happy, Glee, and Joy. These five flamingos are to be distributed to seven different zoos so that no zoo gets both a parent and a child :(. It is not required that every zoo gets a flamingo. In how many different ways can this be done? here if i am using case method on children i am getting a different answer than when i am using case methon on parents, why is that?
Soujit
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in
Combinatory
Apr 5, 2023
by
Soujit
419
views
combinatory
3
votes
2
answers
39
GO Classes 2023 | IIITH Mock Test 1 | Question: 4
How many ways are there to arrange the $12$ letters of $\text{AAABBBBCCCCC}$ without having two $\text{Cs}$ together? $2652$ $1960$ $1826$ $2260$
GO Classes
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Combinatory
Mar 26, 2023
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GO Classes
577
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goclasses2023-iiith-mock-1
goclasses
combinatory
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1-mark
2
votes
1
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40
GO Classes 2023 | IIITH Mock Test 1 | Question: 33
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ where $a_n = \binom {n+4}{n}$ for $n= 0,1,2,\ldots ?$ $\frac{1}{(1-x)^5}$ $\frac{5}{(1-x)}$ $\frac{1}{(1-x)^4}$ $\frac{x}{(1-x)^5}$
GO Classes
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Mar 26, 2023
by
GO Classes
512
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goclasses2023-iiith-mock-1
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