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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

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403
Kenneth Rosen Edition 7 Exercise 6.5 Question 42 (Page No. 433)
In bridge, the $52$ cards of a standard deck are dealt to four players. How many different ways are there to deal bridge hands to four players?
In bridge, the $52$ cards of a standard deck are dealt to four players. How many different ways are there to deal bridge hands to four players?
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0 votes
3 answers
404
Discrete Mathematics
Any Good resource to understand this topic.
Any Good resource to understand this topic.
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3 answers
406
NET nov-17 paper-2 Q8
Let P and Q be two propositions , ~(P<->Q) is equivalent to : a)P<->~Q b)~P<->Q c)~P<->~Q d)Q->P
Let P and Q be two propositions , ~(P<->Q) is equivalent to :a)P<->~Q b)~P<->Q c)~P<->~Q d)Q->P
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5 votes
1 answer
407
Counting number of pairs whose sum is less than k
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k 0$.Solve by summation rules.Solve by combinatorial argument.
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0 votes
1 answer
408
Find Sum of four digit Number
Find the sum of all four digit numbers that can be formed by the digits {0,1,2,3,4}? a)183450 b)259980 c)266640 d)6600
Find the sum of all four digit numbers that can be formed by the digits {0,1,2,3,4}?a)183450b)259980c)266640d)6600
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0 votes
1 answer
409
Kenneth Rosen Edition 7 Exercise 6.1 Question 34 (Page No. 397)
How many different functions are there from a set with $10$ elements to sets with the following numbers of elements? $2$ $3$ $4$ $5$
How many different functions are there from a set with $10$ elements to sets with the following numbers of elements?$2$$3$$4$$5$
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0 votes
1 answer
410
Kenneth Rosen Edition 7 Exercise 6.2 Question 6 (Page No. 405)
Let $d$ be a positive integer. Show that among any group of $d + 1$ (not necessarily consecutive) integers there are two with exactly the same remainder when they are divided by $d.$
Let $d$ be a positive integer. Show that among any group of $d + 1$ (not necessarily consecutive) integers there are two with exactly the same remainder when they are div...
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0 answers
411
MadeEasy Full Length Test: Combinatory - Recurrence
What’s the trick to do it under 2 min here?
What’s the trick to do it under 2 min here?
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0 votes
1 answer
412
rosen excercise
How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 + x6 = 29, where xi , i = 1, 2, 3, 4, 5, 6, is a nonnegative integer such that a) x1 ≤ 5? b) x1 < 8 and x2 > 8?
How many solutions are there to the equationx1 + x2 + x3 + x4 + x5 + x6 = 29,where xi , i = 1, 2, 3, 4, 5, 6, is a nonnegative integer suchthata) x1 ≤ 5?b) x1 < 8 and x...
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0 votes
1 answer
413
In how many ways can 2n+1 seats in a congress be divided among 3 parties ?
In how many ways can $2n+1$ seats in a congress be divided among 3 parties so that coalition of any 2 parties will ensure them majority?
In how many ways can $2n+1$ seats in a congress be divided among 3 parties so that coalition of any 2 parties will ensure them majority?
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0 votes
0 answers
415
Pigeonhole Principle
During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days during which the team must play exactly 14 games.
During a month with 30 days, a baseball team plays at least one game a day, but no morethan 45 games. Show that there must be a period of some number of consecutive days ...
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1 votes
1 answer
416
NIELIT 2022 April Scientist B | Section B | Question: 48
The particular solution of the recurrence relation $a_{r+2} – 4a_{r+1} + 4a_{r} = 2^{r}$ is: $r.2^{r}$ $r(r-1)2^{r-1}$ $r(r-1)2^{r-2}$ $r(r-1)2^{r-3}$
The particular solution of the recurrence relation $a_{r+2} – 4a_{r+1} + 4a_{r} = 2^{r}$ is:$r.2^{r}$$r(r-1)2^{r-1}$$r(r-1)2^{r-2}$$r(r-1)2^{r-3}$
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3 votes
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417
combinatrics
How many 7 length bit strings have atleast 3 consecutive ones?
How many 7 length bit strings have atleast 3 consecutive ones?
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0 votes
2 answers
418
permutations
The number of ways in which 6 rings can be worn on the four fingers of one hand is: a. 360 b. 4^6 c. 6C4 d. 6^4
The number of ways in which 6 rings can be worn on the four fingers of one hand is:a. 360b. 4^6c. 6C4d. 6^4
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0 votes
3 answers
420
Permutations and combinations
In how any ways can 8 different shirts be distributed among 4 different people so that each recieves 2 shirts?
In how any ways can 8 different shirts be distributed among 4 different people so that each recieves 2 shirts?
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