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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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Highest voted questions in Combinatory

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counting
How many bit strings of length 10 contain either five consecutive 0s or five consecutive 1s? I got 382.Is it correct?
How many bit strings of length 10 contain either five consecutive 0s or five consecutive 1s?I got 382.Is it correct?
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5 votes
1 answer
154
How many 4-permutations of the positive integers not exceeding 100 contain three consecutive integers k, k + 1, k + 2,
How many 4-permutations of the positive integers not exceeding 100 contain three consecutive integers k, k + 1, k + 2, in the correct ordera) where these consecutive inte...
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2 answers
163
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 3
Consider the following two combinatorial identities: For all $\mathrm{k}, \mathrm{n} \in \mathrm{N}$ with $\mathrm{k} \leq \mathrm{n}$ ... $1$ Only $2$ Both None
Consider the following two combinatorial identities:For all $\mathrm{k}, \mathrm{n} \in \mathrm{N}$ with $\mathrm{k} \leq \mathrm{n}$,$$\left(\begin{array}{l} n \\ 2 \end...
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4 votes
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165
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 14
The number of ways of selecting at least one Indian and at least one American for a debate from a group comprising $3$ Indians and $4$ Americans and no one else?
The number of ways of selecting at least one Indian and at least one American for a debate from a group comprising $3$ Indians and $4$ Americans and no one else?
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4 votes
1 answer
170
GATE Overflow Test Series | Mock GATE | Test 3 | Question: 27
How many different one-to-one functions $f : \{0, 1, \ldots, n\} \rightarrow \{0, 1,\ldots , n+1\}$ are there? $ ^nP_{n+2}$ $^{n+1}P_{n+2}$ $^{n+2}P_{n+1}$ None of the above
How many different one-to-one functions $f : \{0, 1, \ldots, n\} \rightarrow \{0, 1,\ldots , n+1\}$ are there?$ ^nP_{n+2}$$^{n+1}P_{n+2}$$^{n+2}P_{n+1}$None of the above
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