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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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Most viewed questions in Combinatory

3 votes
1 answer
501
Seldon Ross
How many 5 digit numbers can be formed from the integers 1,2......9 if no digit can appear more than twice?
How many 5 digit numbers can be formed from the integers 1,2......9 if no digit can appear more than twice?
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1 votes
2 answers
502
NET 2015 Paper 2
How many solutions are there for the equation $x+y+z+u=29,\, x\geq 1,y\geq 2,z\geq 3,u\geq 0$ ?
How many solutions are there for the equation $x+y+z+u=29,\, x\geq 1,y\geq 2,z\geq 3,u\geq 0$ ?
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0 votes
1 answer
503
Permutation1.1
If there are 9 students in a class and each team contain 3 students then how many number of ways 9 students can be partitioned into 3 teams? Why is this not 9C3*6C3*3C3?
If there are 9 students in a class and each team contain 3 students then how many number of ways 9 students can be partitioned into 3 teams?Why is this not 9C3*6C3*3C3?
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0 votes
1 answer
504
COMBINATION
How many ways are there to select five bills from a cash box containing $1 bills, $2 bills, $5 bills, $10 bills, $20 bills, $ ... THE SOLUTION SPECIFIED IN KENETH ROSEN.......... DOUBT IS WHY THIS CAN BE SOLVE USING METHOD OF FINDING NON NEGATIVE INTEGRAL SOLUTION POSSIBLE
How many ways are there to select five bills from a cash box containing $1 bills, $2 bills, $5bills, $10 bills, $20 bills, $50 bills, and $100 bills? Assume that the orde...
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0 votes
1 answer
505
Kenneth Rosen Edition 7 Exercise 6.5 Question 23 (Page No. 432)
How many ways are there to distribute $12$ distinguishable objects into six distinguishable boxes so that two objects are placed in each box?
How many ways are there to distribute $12$ distinguishable objects into six distinguishable boxes so that two objects are placed in each box?
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1 votes
1 answer
506
Discrete mathematics
The non-negative integral solutions to the equation $x_1+x_2+x_3+x_4 \leq10$
The non-negative integral solutions to the equation$x_1+x_2+x_3+x_4 \leq10$
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0 votes
1 answer
507
Rosen Ex.6.1
Find a recurrence relation for the number of ways to lay out a walkway with slate tiles if the tiles are red, green, or gray so that no two red tiles are adjacent and tiles of the same color are considered indistinguishable
Find a recurrence relation for the number of ways to lay out a walkway with slate tiles if thetiles are red, green, or gray so that no two red tiles are adjacent and tile...
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2 votes
2 answers
508
Kenneth Rosen Edition 6th Exercise 5.5 Question 33 (Page No. 380)
Question How many different strings of length 2 can be made from the letters in 'ORONO'? I am getting 7 strings as follows: OO, ON, OR, NO, RO, RN, NR but given answer is 6.
Question How many different strings of length 2 can be made from the letters in 'ORONO'?I am getting 7 strings as follows: OO, ON, OR, NO, RO, RN, NRbut given answer is 6...
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0 votes
1 answer
509
In a round-robin tournament with m players, every two players play one game in which one player wins and the other loses.
In a round-robin tournament with m players, every two players play one game in which one player wins and the other loses. We want to find conditions on positive integers ...
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3 votes
1 answer
510
Permutation and combination
in how many ways 2 alike apple, 3 alike orange and 4 alike mango can be given to 3 children if each child can have none or 1 or more than 1 fruits.
in how many ways 2 alike apple, 3 alike orange and 4 alike mango can be given to 3 children if each child can have none or 1 or more than 1 fruits.
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3 votes
1 answer
511
How to solve such problem?
How many solution exist for x+y+z=10 with 1<=x<4 1<=y<=7 and z>1
How many solution exist for x+y+z=10 with 1<=x<4 1<=y<=7 and z>1
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0 votes
1 answer
513
Number Of Substrings | Made Easy Test Series
The number of subwords for w=’SCALABLE” is equal to: 34 35 37
The number of subwords for w=’SCALABLE” is equal to:343537
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0 votes
0 answers
514
ISI 2018 MMA 1
The number of common terms in the two sequence (3,7,11,...,407} and {2,9,16,...,70} is A)13 B)14 C)15 D)16
The number of common terms in the two sequence (3,7,11,...,407} and {2,9,16,...,70} isA)13 B)14C)15D)16
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0 votes
0 answers
516
derangement
consider 5 numbered balls and 5 numbered boxes , how many ways are possible such that exactly 2 balls is not on the ith spot ? [Ball i is in the ith box ]
consider 5 numbered balls and 5 numbered boxes , how many ways are possible such that exactly 2 balls is not on the ith spot ?[Ball i is in the ith box ]
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1 votes
1 answer
517
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
2 answers
520
Counting problem
If I have 4 digit number formed using 5,6,7,8. What is the sum of all such 4 digit numbers? Please provide the detailed solution, I am unable to follow counting problems. Thank You.
If I have 4 digit number formed using 5,6,7,8. What is the sum of all such 4 digit numbers?Please provide the detailed solution, I am unable to follow counting problems. ...
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