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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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#1
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Counting
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 ... the class must have at least three male students or at least seven femalestudents.
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#2
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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 ... probability that if $A$ starts the rumor, then $A$ receives the third calls?
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#3
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6 votes
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 56
The coefficient of $x^6$ in the expansion of $A(x)$ is, where$A(x)=\frac{x(1+x)}{(1-x)^3}$
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#4
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#self doubt
Can someone please explain the following case of combinationI means identicalD means different DOIB with boxes being empty and non emptyAs in this question the given ... .in/420251/go-classes-test-series-2024-mock-gate-test-12-question-17
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#5
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4 votes
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 ... $10^{20}-2^{10}$ $\dfrac{20 ! 10 !}{2^{10}}$
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#6
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GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 17
The number of ways that one can divide $10$ distinguishable objects into $3$ ... In how many different ways can one do this if the piles are also distinguishable?
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#7
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GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 18
The number of ways that one can divide $10$ distinguishable objects in $3$ ... In how many different ways can one do this if the objects are also indistinguishable?
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#8
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7 votes
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 ... $k \geq 3$.What is $a+ b?$
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#9
240
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selfdoubt combinatory
In how many ways can you distribute 4 different choclates to 3 people such that each gets atleast 1 choclate.
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#11
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#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 ... above cases will be included in either or case or only 1,2 will be included?
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#12
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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
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#13
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GoClasses Youtube
Determine the Number of $6$ digit integers (no leading zeroes) in which no digit is repeated and its divisible by $4$.
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#14
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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 ? 3666105None
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#15
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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 $\text{all}$ of these letters. ... ) How many words have all letters distinct?d) How many arrangements have no two vowels consecutive?
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#16
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Byjus Workbook
Sir I am getting answer as 25my approach k+1=3k=2n=12nk+1=25@sachinmittal1@gate_cse
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#17
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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 ?
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#18
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Self Doubt on Combinatory Discrete Mathematics
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 such that you take at least one from each basket ?
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#19
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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.
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#20
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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 ?
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