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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

0 votes
2 answers
261
A closet has 5 pair of shoes.
A closet has 5 pair of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be no complete pair is
A closet has 5 pair of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be no complete pair is
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2 votes
2 answers
262
Generating function
The coefficient of in the expansion of is
The coefficient of in the expansion of is
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0 votes
2 answers
263
#first course in probability #sheldon_ross
In how many ways can 3 boys and 3 girls can sit together such that ONLY boys should together?
In how many ways can 3 boys and 3 girls can sit together such that ONLY boys should together?
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4 votes
2 answers
264
Mathematics
In how many different ways 10 identical ball can be distributed among 3 children, if each receives atleast 2 balls and no more than 4 balls?
In how many different ways 10 identical ball can be distributed among 3 children, if each receives atleast 2 balls and no more than 4 balls?
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2 votes
2 answers
265
Mathmatics problem
how many 4 digit numbers possible whose sum is equal to 12 ?
how many 4 digit numbers possible whose sum is equal to 12 ?
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2 votes
2 answers
266
answer 90 or 444?
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1 votes
2 answers
267
Rosen-Advance Counting Technique-26
Find a recurrence relation for the number of bit strings of length $n$ that contain the string $01.$ I am getting a recurrence like An = 2^(n-2) + 2A(n-1) - A (N-2) .Answer is not given for this question.Please help and explain your steps.
Find a recurrence relation for the number of bit strings of length $n$ that contain the string $01.$I am getting a recurrence like An = 2^(n-2) + 2A(n-1) - A (N-2) .Answe...
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4 votes
2 answers
269
Generating Function
Find the coefficient of $x^{83}$ in $(x^5+ x^8+ x^{11}+ x^{14}+ x^{17})^{10} ?$
Find the coefficient of $x^{83}$ in $(x^5+ x^8+ x^{11}+ x^{14}+ x^{17})^{10} ?$
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2 votes
2 answers
270
Combinatorics Doubt
A box contain 10 screws out of which 3 are defective.If two screws are drawn at random WITH REPLACEMENT.What is the probability that no screw is defective? Answer given as 7c2/10C2 my question is ,as its given With Replacement. So why not it is (7/10)*(7/10)
A box contain 10 screws out of which 3 are defective.If two screws are drawn at random WITH REPLACEMENT.What is the probability that no screw is defective?Answer given as...
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1 votes
2 answers
271
Recurrence Relation
The recurrence relation for the number of n-digit quaternary sequences that have an even number of zeros (quaternary sequences use only 0,1,2,3 for digits) is- (A) an = an-1 + 4n-1 (B) an = 3an-1 + 4n-1 (C) an = 2an-1 + 4n-1 (D) an = an-1 + 4n-2
The recurrence relation for the number of n-digit quaternary sequences that have an even number of zeros (quaternary sequences use only 0,1,2,3 for digits) is-(A) an = an...
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4 votes
2 answers
273
Generating function
Find $\large\color{maroon}{a^n}$ for the following generating function, $\color{green}{\begin{align*} \frac{1}{1-2x^2} \end{align*}}$ $\large\color{maroon}{a^n}$ = closed form of the $nth$ term in the corresponding sequence.
Find $\large\color{maroon}{a^n}$ for the following generating function,$$\color{green}{\begin{align*} \frac{1}{1-2x^2} \end{align*}}$$$\large\color{maroon}{a^n}$ = closed...
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3 votes
2 answers
274
Testbook
In how many ways 10 different books can be distributed among there students A, B and C such that A must be given at least 1 book?
In how many ways 10 different books can be distributed among there students A, B and C such that A must be given at least 1 book?
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15 votes
2 answers
276
TIFR CSE 2017 | Part A | Question: 6
How many distinct words can be formed by permuting the letters of the word $\text{ABRACADABRA}?$ $\frac{11!}{5! \: 2! \: 2!}$ $\frac{11!}{5! \: 4! }$ $11! \: 5! \: 2! \: 2!\:$ $11! \: 5! \: 4!$ $11! $
How many distinct words can be formed by permuting the letters of the word $\text{ABRACADABRA}?$$\frac{11!}{5! \: 2! \: 2!}$$\frac{11!}{5! \: 4! }$$11! \: 5! \: 2! \: 2!\...
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3 votes
2 answers
277
Permutation and combination
The number of ways can 10 balls be selected from urn contain 10 identical red balls 5 identical green balls and 3 identical blue balls ?
The number of ways can 10 balls be selected from urn contain 10 identical red balls 5 identical green balls and 3 identical blue balls ?
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17 votes
2 answers
279
Generalized permutation and combination
How many positive integers less than 1,000,000 have the sum of their digits equal to 19? (using generating function)
How many positive integers less than 1,000,000 have the sum of their digits equal to 19? (using generating function)
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12 votes
2 answers
280
GATE CSE 1990 | Question: 3-ix
The number of ways in which $5\; A's, 5\; B's$ and $5\; C's$ can be arranged in a row is: $15!/(5!)^{3}$ $15!$ $\left(\frac{15}{5}\right)$ $15!(5!3!)$.
The number of ways in which $5\; A's, 5\; B's$ and $5\; C's$ can be arranged in a row is:$15!/(5!)^{3}$$15!$$\left(\frac{15}{5}\right)$$15!(5!3!)$.
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