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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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Most viewed questions in Combinatory

0 votes
2 answers
362
basic aptitude
12 chairs are arranged in a row and are numbered 1 to 12 4 men have to be seated in these chairs so that the chairs numbered 1 and 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done. A. 360 B. 384 C. 432 D. 470
12 chairs are arranged in a row and are numbered 1 to 12 4 men have to be seated in these chairs so that the chairs numbered 1 and 8 should be occupied and no two men occ...
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2 votes
1 answer
363
permutation & combination
if no 3 diagonal of a convex decagon meet at the same point inside the decagon ,into how many line segments are the diagonal divided by their intersection?
if no 3 diagonal of a convex decagon meet at the same point inside the decagon ,into how many line segments are the diagonal divided by their intersection?
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2 votes
1 answer
364
#Discrete #Combinatorics
The number of ways in which n distinct objects can be put into two identical boxes so that no box remains empty, is a) 2^n - 1 b) 2^n - 2 c) 2^(n-1) - 1 d) None of these Please explain your answer.
The number of ways in which n distinct objects can be put into two identical boxes so that no box remains empty, isa) 2^n - 1b) 2^n - 2c) 2^(n-1) - 1d) None of thesePleas...
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0 votes
2 answers
366
Suppose a 6 digit number N is formed by rearranging the digits of the number 123456
Suppose a 6 digit number N is formed by rearranging the digits of the number 123456. If N is divisible by 5, then the set of all possible remainders when N is divided by 45 is (A) {30} (B) {15, 30} (C) {0,15,30} (D) {0, 5, 15, 30}
Suppose a 6 digit number N is formed by rearranging the digits of the number 123456. If N is divisible by 5, then the set of all possibleremainders when N is divided by 4...
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2 votes
3 answers
368
P and C doubt
Given a 4 *4 grid points , how many Triangles with vertices on the grid can be formed?
Given a 4 *4 grid points , how many Triangles with vertices on the grid can be formed?
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0 votes
1 answer
370
Question on combinatorics
Given solution of this question: I think that number of 5 elements subsets with 7 should be C(n-1, 4) instead of C(n,4) as we have already fixed 7 so number of elements left will be n-1. Please check
Given solution of this question:I think that number of 5 elements subsets with 7 should be C(n-1, 4) instead of C(n,4) as we have already fixed 7 so number of elements le...
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0 votes
3 answers
372
Self doubt generating function
Equation: $x+y=10$ and we are asked to find out the number of a non-negative integral solution of this equation.
Equation: $x+y=10$ and we are asked to find out the number of a non-negative integral solution of this equation.
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1 votes
2 answers
374
Rosen 7e Exercise-8.5 Question-15 page no-558 Inclusion-Exclusion
How many permutations of the 10 digits either begin with the 3 digits 987, contain the digits 45 in the fifth and sixth positions, or end with the 3 digits 123?
How many permutations of the 10 digits either begin with the 3 digits 987, contain the digits 45 in the fifth and sixth positions, or end with the 3 digits 123?
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0 votes
1 answer
375
Kenneth Rosen Edition 7 Exercise 6.5 Question 12 (Page No. 432)
How many different combinations of pennies, nickels, dimes, quarters, and half dollars can a piggy bank contain if it has $20$ coins in it?
How many different combinations of pennies, nickels, dimes, quarters, and half dollars can a piggy bank contain if it has $20$ coins in it?
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