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Syllabus: Combinatorics: Counting, Recurrence relations, Generating functions.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&1&0&0&2&1&0&0&1&0&0&0.6&2
\\\hline\textbf{2 Marks Count} & 2 &0&1&1&0&1&0&1&2&1&0&0.9&2
\\\hline\textbf{Total Marks} & 5 &1&2&2&2&3&0&2&5&2&0&2.4&5\\\hline
\end{array}}}$$

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Questions without an upvoted answer in Combinatory

1 votes
1 answer
2
selfdoubt combinatory
In how many ways can you distribute 4 different choclates to 3 people such that each gets atleast 1 choclate.
In how many ways can you distribute 4 different choclates to 3 people such that each gets atleast 1 choclate.
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0 votes
4 answers
4
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
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
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0 votes
1 answer
5
Byjus Workbook
Sir I am getting answer as 25 my approach k+1=3 k=2 n=12 nk+1=25 @sachinmittal1 @gate_cse
Sir I am getting answer as 25my approach k+1=3k=2n=12nk+1=25@sachinmittal1@gate_cse
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0 votes
0 answers
6
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 ?
What is the total number of integer partitions ( unordered Summation) of the natural number 8 ?I am getting 22. Is it correct ?
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0 votes
1 answer
7
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 ?
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 ?...
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1 votes
0 answers
10
kenneth rosen, counting, exercise: 6.5, question: 50
How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?
How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?
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0 votes
0 answers
17
Unacademy AIMT 1
How many integers are there in the set {1,2,3,…..,1000} with no digit being repeated?
How many integers are there in the set {1,2,3,…..,1000} with no digit being repeated?
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1 votes
0 answers
18
DRDO CSE 2022 Paper 1 | Question: 14
Derangements are permutations $\pi$ of the set $\{1,2, \ldots, n\}$ such that $\pi(i) \neq i.$ Compute the number of derangements on the set $1,2, \ldots, n$.
Derangements are permutations $\pi$ of the set $\{1,2, \ldots, n\}$ such that $\pi(i) \neq i.$ Compute the number of derangements on the set $1,2, \ldots, n$.
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1 votes
0 answers
19
DRDO CSE 2022 Paper 1 | Question: 16
Let us say we have a supply of $1$ rupee and $2$ rupee coins in large quantities. What is the generating function for the number of ways of giving change with $1$ rupee and $2$ rupee coins.
Let us say we have a supply of $1$ rupee and $2$ rupee coins in large quantities. What is the generating function for the number of ways of giving change with $1$ rupee a...
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2 votes
1 answer
20
DRDO CSE 2022 Paper 1 | Question: 18
A gardener wants to buy $3$ neem plants, $5$ rose plants and $1$ banyan plant from a nursery having $7$ neem, $10$ rose and $6$ banyan plants. How many choices does a gardener have?
A gardener wants to buy $3$ neem plants, $5$ rose plants and $1$ banyan plant from a nursery having $7$ neem, $10$ rose and $6$ banyan plants. How many choices does a gar...
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1 votes
1 answer
21
DRDO CSE 2022 Paper 1 | Question: 19
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$
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0 votes
0 answers
22
Engineering Mathematics
Can somebody brief description about this topic(means formula or link to study). Actually this question is asked in TOC test, but looking more like mathematics part.
Can somebody brief description about this topic(means formula or link to study).Actually this question is asked in TOC test, but looking more like mathematics part.
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6 votes
0 answers
23
Combinatorics : Distinct objects and Distinct boxes
How many ways are there to Distribute 7 distinct objects to 3 Distinct boxes and No box should be Empty Any box can be Empty
How many ways are there to Distribute 7 distinct objects to 3 Distinct boxes andNo box should be EmptyAny box can be Empty
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0 votes
0 answers
24
Mathematics for Natural Science
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$
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0 votes
3 answers
25
Discrete Mathematics
Any Good resource to understand this topic.
Any Good resource to understand this topic.
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0 votes
0 answers
26
Discrete Mathematics and Combinatorics
Solve the recurrence relation $a^{2}n-5a^{2}_{n-1}+4a^{2} _{n-2}=0$, if $a_{0}=4, a_{1}=13, n>1$
Solve the recurrence relation $a^{2}n-5a^{2}_{n-1}+4a^{2} _{n-2}=0$, if $a_{0}=4, a_{1}=13, n>1$
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0 votes
1 answer
27
A question paper is divided into two parts A and B and each part contains 5 questions. In how many ways a student can answer the question paper, if he has to solve total 6 questions including atleast 2 from each section.
I solved the question using the logic first select two questions from each sections. ($\binom{5}{2} * \binom{5}{2}$). Then from remaining 6 questions choose any 2. theref...
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1 votes
1 answer
29
NPTEL Assignment Question
The number of possible subsequences in a string of length n are: $n^{2}$ $2^{n}$ n! n(n-1)
The number of possible subsequences in a string of length n are:$n^{2}$$2^{n}$ n!n(n-1)
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0 votes
1 answer
30
gateacademy testseries
In how many ways can seven different jobs be assigned to four different employees so that each employee is assigned at least one job and the most difficult job is assigned to the best employee?
In how many ways can seven different jobs be assigned to four different employees so that each employee is assigned at least one job and the most difficult job is assigne...
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