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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 answered questions in Combinatory

–1 votes
2 answers
201
Aai it 2018
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0 votes
2 answers
203
Permutation and combination
9 different books are to be arranged on a bookshelf. 4 of these books were written by Shakespeare, 2 by Dickens, and 3 by Conrad. How many possible permutations are there if the books by Conrad must be separated from one another?
9 different books are to be arranged on a bookshelf. 4 of these books were written by Shakespeare, 2 by Dickens, and 3 by Conrad. How many possible permutations are there...
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2 votes
2 answers
204
test series(combinatorics)
Q.1) The number of integral solution of equation X1+X2+X3+X4=20 where X1>=3,X2>=1,X3>=0,X4>=5 is................... can anyone explain the approach to solve this question???
Q.1) The number of integral solution of equation X1+X2+X3+X4=20 where X1>=3,X2>=1,X3>=0,X4>=5 is...................can anyone explain the approach to solve this question...
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0 votes
2 answers
205
Recurrence Relation
Let $T(n) = T(n-1) + \frac{1}{n} , T(1) = 1 ;$ then $T(n) = ? $ $O(n^{2})$ $O(logn)$ $O(nlogn)$ $O(n^{2}logn)$
Let $T(n) = T(n-1) + \frac{1}{n} , T(1) = 1 ;$ then $T(n) = ? $$O(n^{2})$$O(logn)$$O(nlogn)$$O(n^{2}logn)$
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2 votes
2 answers
207
Kenneth Rosen Edition 6th Exercise 6.4 Question 7g (Page No. 440)
Please tell me the approach of solving the question for finding a closed formula for the given generating function:- $x^{2} / (1-x)^{2}$ . Please determine the general approach how to solve
Please tell me the approach of solving the question for finding a closed formula for the given generating function:-$x^{2} / (1-x)^{2}$ . Please determine the general app...
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0 votes
2 answers
208
Classroom
How many 5 letter (lower case) passwords are possible with with at least 2 'a's?
How many 5 letter (lower case) passwords are possible with with at least 2 'a's?
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0 votes
2 answers
211
Combinatorics-Self Doubt
Number of ways to distribute 5 distinct toys to 3 children A,B,C such that each one of them gets atleast one toy. My answer come to be 75.Is it correct? Also, when toys are not distinct, will answer change?
Number of ways to distribute 5 distinct toys to 3 children A,B,C such that each one of them gets atleast one toy.My answer come to be 75.Is it correct? Also, when toys ar...
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2 votes
2 answers
212
Rolling of a dice
The number of ways to roll 5 six sided dice to get sum of 25 is ________. _________________________________________________________ if solving with generating function, then why dividing by $\left ( 1-x \right )$ if equation is $\frac{x\left ( 1-x^{6} \right )}{\left ( 1-x \right )}$?
The number of ways to roll 5 six sided dice to get sum of 25 is ________._________________________________________________________if solving with generating function, the...
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2 votes
2 answers
213
Permutations with restrictions
$Z =\left \{ {A,B,C,D,E,F,G} \right \}$ How many permutations of all elements of set $Z$ are possible when A cannot appear after D and C cannot appear after F C cannot appear after D
$Z =\left \{ {A,B,C,D,E,F,G} \right \}$How many permutations of all elements of set $Z$ are possible when A cannot appear after D and C cannot appear after FC cannot appe...
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4 votes
2 answers
214
MADEEASY
Consider a set S={1000,1001,1002........,9999}. The numbers in set S having atleast one digit as 2 and atleast one digit as 5 are?
Consider a set S={1000,1001,1002........,9999}. The numbers in set S having atleast one digit as 2 and atleast one digit as 5 are?
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1 votes
2 answers
215
Zeal Workbook: Combinatory - Permutations & Combinations
$\text{How many 5 letter word can be formed}$ $\text{from 6 a's,6 b's,6 c's,5 d's,5e's,4f's,4g's,3h's,3i's ?}$
$\text{How many 5 letter word can be formed}$$\text{from 6 a's,6 b's,6 c's,5 d's,5e's,4f's,4g's,3h's,3i's ?}$
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1 votes
2 answers
218
Pigeon hole
Show that in a group of $n$ people there are two who have identical number of friends in that group.
Show that in a group of $n$ people there are two who have identical number of friends in that group.
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1 votes
2 answers
219
Generating Function
Find $\left [ x^{50} \right ]$ $\left ( x^{6}+x^{7}+x^{8}+.... \right )^{6}$
Find $\left [ x^{50} \right ]$$\left ( x^{6}+x^{7}+x^{8}+.... \right )^{6}$
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0 votes
2 answers
220
combinatorics
There were 4 blue french horns, 5 yellow Umbrellas and 6 Suits in a shop. Ted, Barney, Lily, Marshal and Robin came to the shop to buy the items. How many different results could have been recorded if all of the items were sold?
There were 4 blue french horns, 5 yellow Umbrellas and 6 Suits in a shop. Ted, Barney, Lily, Marshal and Robin came to the shop to buy the items. How many different resul...
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