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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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Recent questions in Combinatory

0 votes
1 answer
861
Combinatorics
How many ways we can move from a point (a,b) to a point (i,j) in a coordinate system. Here i>a and j>b and at each step you can move to the right or in the upward direction.
How many ways we can move from a point (a,b) to a point (i,j) in a coordinate system. Here i>a and j>b and at each step you can move to the right or in the upward directi...
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862
Testbook Test Series: Combinatory - Permutations And Combinations
NUMBER OF WAYS IN WHICH CORNER OF THE SQUARE CAN BE COLORED WITH TWO COLORS. (ITS IS PERMISSIBLE TO USE A SINGLE COLOUR ON ALL FOUR CORNER)
NUMBER OF WAYS IN WHICH CORNER OF THE SQUARE CAN BE COLORED WITH TWO COLORS. (ITS IS PERMISSIBLE TO USE A SINGLE COLOUR ON ALL FOUR CORNER)
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1 votes
1 answer
863
Testbook Test Series: Combinatory - Permutations And Combinations
NUMBER OF WAYS WE CAN ARRAYS LETTERS OF THE WORD "TESTBOOK" SO THAT NO TWO VOWELS ARE TOGETHER IS
NUMBER OF WAYS WE CAN ARRAYS LETTERS OF THE WORD "TESTBOOK" SO THAT NO TWO VOWELS ARE TOGETHER IS
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1 votes
0 answers
864
Permutation of 4 Gs out of 5 Gs
Given symbols:- $GGGGGAAATTTECCS$ No of ways such that exactly 4 Gs out of 5 Gs are together. I am getting$ \frac{11! × 11}{3!×3!×2!} $. Some one verify it?
Given symbols:- $GGGGGAAATTTECCS$No of ways such that exactly 4 Gs out of 5 Gs are together. I am getting$ \frac{11! × 11}{3!×3!×2!} $.Some one verify it?
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1 votes
1 answer
865
Kenneth Rosen Edition 6th Exercise 6.4 Question 33 (Page No. 442)
Use generating function to solve the recurrence relation $a_k=3{a_{k-1}} + 2$ with initial conditions $a_0=1 $.
Use generating function to solve the recurrence relation $a_k=3{a_{k-1}} + 2$ with initial conditions $a_0=1 $.
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1 votes
1 answer
866
Permutations
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2 votes
2 answers
870
Generating functions
What will be the coefficient of x^17 in the expansion of (x+x^2+x^3+x^4+x^5+x^6)^4?
What will be the coefficient of x^17 in the expansion of (x+x^2+x^3+x^4+x^5+x^6)^4?
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2 votes
2 answers
872
Kenneth Rosen Edition 6th Exercise 5.5 Question 35 (Page No. 380)
How many strings with seven or more characters can be formed from the letters of the word $\text{EVERGREEN}$ ?
How many strings with seven or more characters can be formed from the letters of the word $\text{EVERGREEN}$ ?
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0 answers
874
self doubt
Three men have 4 coats, 5 waist coats, and 6 caps. In how many ways can they wear them? Three men have 4 coats, 5 waist coats, and 6 caps. In how many ways can they wear any type of them?
Three men have 4 coats, 5 waist coats, and 6 caps. In how many ways can they wear them?Three men have 4 coats, 5 waist coats, and 6 caps. In how many ways can they wear ...
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2 votes
0 answers
875
Number of unique solution
Suppose there is an equation $x_{1}+x_{2}+...........x_{r}=n$ Then number of unique solution in this given equation?
Suppose there is an equation$x_{1}+x_{2}+...........x_{r}=n$Then number of unique solution in this given equation?
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0 votes
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879
Combinatorics
There are total 21 identical balls in a shop and 7 children. In how many ways can 7 children claim the balls? (it is not necessary to claim all the balls)
There are total 21 identical balls in a shop and 7 children. In how many ways can 7 children claim the balls? (it is not necessary to claim all the balls)
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1 votes
3 answers
880
Kenneth Rosen Edition 6th Exercise 5.5 Example 10 (Page No. 377)
How many ways are there to put four different employees into three indistinguishable offices when each office can contain any number of employees?
How many ways are there to put four different employees into three indistinguishable offices when each office can contain any number of employees?
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