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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

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1 answer
393
Kenneth Rosen Edition 7 Exercise 6.4 Question 2 (Page No. 421)
Find the expansion of $(x + y)^{5}$ using combinatorial reasoning, as in Example $1.$ using the binomial theorem.
Find the expansion of $(x + y)^{5}$using combinatorial reasoning, as in Example $1.$using the binomial theorem.
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0 votes
1 answer
394
Cool 6-Digit Numbers
Let us call a -digit number cool if each of its digits is no less than the preceding digit. How many cool $6-$digit numbers are there? Details And Assumptions: For example, $,112446 is cool. 233043 isn't cool.
Let us call a -digit number cool if each of its digits is no less than the preceding digit. How many cool $6-$digit numbers are there?Details And Assumptions:For example,...
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1 votes
1 answer
396
Kenneth Rosen Edition 7 Exercise 6.1 Question 13 (Page No. 396)
How many bit strings with length not exceeding $n,$ where $n$ is a positive integer, consist entirely of $1s,$ not counting the empty string?
How many bit strings with length not exceeding $n,$ where $n$ is a positive integer, consist entirely of $1s,$ not counting the empty string?
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0 votes
3 answers
400
Discrete Mathematics
Any Good resource to understand this topic.
Any Good resource to understand this topic.
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3 votes
2 answers
401
Permutation and combination
The number of ways can 10 balls be selected from urn contain 10 identical red balls 5 identical green balls and 3 identical blue balls ?
The number of ways can 10 balls be selected from urn contain 10 identical red balls 5 identical green balls and 3 identical blue balls ?
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0 votes
3 answers
402
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
403
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
404
Kenneth Rosen Edition 7 Exercise 6.1 Question 45 (Page No. 397)
How many ways are there to seat six people around a circular table where two seating are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors?
How many ways are there to seat six people around a circular table where two seating are considered the same when everyone has the same two neighbors without regard to wh...
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0 votes
1 answer
406
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
1 answer
407
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
408
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 votes
1 answer
409
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
1 answer
410
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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