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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2024-1} & \textbf{2024-2} & \textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &0&0&1& 1&1&0&0&0.5&1
\\\hline\textbf{2 Marks Count} &0&0&1& 2 &0&1&0&0.67&2
\\\hline\textbf{Total Marks} & 0&0&3&5 &1&2&0&1.83&5\\\hline
\end{array}}}$$

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Questions without a selected answer in Combinatory

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1
Counting
Suppose that there are nine students in a discrete mathematics class at a small college. a) Show that the class must have at least five male students or at least five female students. b) Show that the class must have at least three male students or at least seven female students.
Suppose that there are nine students in a discrete mathematics class at a smallcollege.a) Show that the class must have at least five male students or at least five femal...
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1 votes
1 answer
8
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
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
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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2 votes
4 answers
12
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
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 ? 3666105None
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0 votes
1 answer
14
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
15
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
16
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 ?
Given there are 3 full baskets of apples, mangoes, and oranges. How many ways possible ifa) You need to buy any 4 fruits out of these 3 baskets ?b) you buy any 4 fruits s...
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1 answer
17
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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2 votes
1 answer
20
GO Classes 2024 | IIITH Mock Test 5 | Question: 39
The minimum number of integers to be selected from the set $S = \{1, 2, \dots , 9\}$ so that the difference of at least two of the integers is guaranteed to be $5$ is ______ $4$ $5$ $6$ $7$
The minimum number of integers to be selected from the set $S = \{1, 2, \dots , 9\}$ so that the difference of at least two of the integers is guaranteed to be $5$ is ___...
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3 votes
2 answers
21
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? $2652$ $1960$ $1826$ $2260$
How many ways are there to arrange the $12$ letters of $\text{AAABBBBCCCCC}$ without having two $\text{Cs}$ together?$2652$$1960$$1826$$2260$
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1 votes
0 answers
23
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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1 votes
1 answer
29
#Combinatorics #Self doubt
How many 3 digits number are there which are divisible by 3 and repetition of digits NOT allowed.?
How many 3 digits number are there which are divisible by 3 and repetition of digits NOT allowed.?
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7 votes
4 answers
30
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 $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
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 $L_{2}=3$.Which one of t...
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