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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
302
Dividing a set of n elements in r groups where groups are of size n1,n2,n3... and n1+n2+n3+ ...(uo to r terms ) = n
(Reference- A first course in probablity by Sheldon Ross [Example 5b and 5c of chapter 1])Q1. Ten children are to be divided into an A team and a B team of 5 each. The A ...
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0 votes
2 answers
304
ISI 2016
an is a n-digit number of 0's and 1's with no consecutive 0's i.e., without the occurrence of '00'. For example, a8 =10111011. Construct a recurrence relation for an(a0=1).
an is a n-digit number of 0's and 1's with no consecutive 0's i.e., without the occurrence of '00'. For example, a8 =10111011. Construct a recurrence relation for an(a0=1...
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1 votes
2 answers
305
Different color combination of identical balls
There are three identical red balls and four identical blue balls in bag.Three balls are drawn.what is the number of different color combinations ?
There are three identical red balls and four identical blue balls in bag.Three balls are drawn.what is the number of different color combinations ?
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1 votes
2 answers
306
circular arrangement
how many ways are there to arrange 6 girls and 15 boys in a circle such that there are atleast two boys between two adjacent girls?
how many ways are there to arrange 6 girls and 15 boys in a circle such that there are atleast two boys between two adjacent girls?
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0 votes
2 answers
308
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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3 votes
2 answers
309
Recurrance Relation
an = an-1 + n , n>=1 a0=2 Find a100... ? Solution I actually wanted to know what is wrong with this method . Could you pls help Whats wrong here . T(n) = T(n-1)+n and back substitute T(n)= T(n-k) + nk putting n-k = 0 T(n) = 2+ n* n So T(100) = 2+100*100 Actual answer is 5052
an = an-1 + n , n>=1a0=2Find a100... ?SolutionI actually wanted to know what is wrong with this method .Could you pls help Whats wrong here .T(n) = T(n-1)+nand back su...
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2 votes
2 answers
310
Question on permutation and combination
Given answer: B, Please explain me how to solve it.
Given answer: B, Please explain me how to solve it.
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1 votes
2 answers
311
permutation
for aaaabbbcccdde find no of permutation such that 1)no two c are together 2)no 3 c are consecutive
for aaaabbbcccdde find no of permutation such that 1)no two c are together2)no 3 c are consecutive
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0 votes
2 answers
312
How many 4 digit integers are there with digit 6 appearing exactly once
How many 4 digit integers are there with digit 6 appearing exactly once . 6_ _ _ 9 *8*7 _ 6 _ _ 9* 8 * 7 _ _ 6 _ 9*9*7 _ _ _ 6 9*9*8 I'm getting as 2223 . Is my approach correct . In book I'm getting a different ans .
How many 4 digit integers are there with digit 6 appearing exactly once .6_ _ _ 9 *8*7_ 6 _ _ 9* 8 * 7_ _ 6 _ 9*9*7_ _ _ 6 9*9*8I'm getting as 2223 .Is my approach c...
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0 votes
2 answers
313
How do one know permutation or combination to be used in a question ?
Suppose if we have 6 Different English movies 8 Different Malayalam Movies 10 Different Hindi Movie How many ways we can choose 2 movies of different languages ? How do one know Permutation or combination is to be used in a question ?
Suppose if we have6 Different English movies8 Different Malayalam Movies10 Different Hindi MovieHow many ways we can choose 2 movies of different languages ?How do one kn...
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0 votes
2 answers
314
Commitee.
Find number of ways of selecting a commitee of 10 members out of 6 men and 7 women of which atleast 4 women are included. a)231 b)25200 c)325 d)286
Find number of ways of selecting a commitee of 10 members out of 6 men and 7 women of which atleast 4 women are included.a)231 b)25200 c)325 d)286
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1 votes
2 answers
315
Probability question on a pair of dice
I think the ans should be C, but the given answer is A. Anyone can explain please?
I think the ans should be C, but the given answer is A. Anyone can explain please?
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3 votes
2 answers
316
Counting number of functions which are neither 1-1 nor onto
Let $A = \left \{1, 2, 3, 4 \right \}$. Number of functions possible on $A$ which are neither $1-1$ nor on-to is _________.
Let $A = \left \{1, 2, 3, 4 \right \}$. Number of functions possible on $A$ which are neither $1-1$ nor on-to is _________.
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1 votes
2 answers
317
Question on rolling fair dice
Given answer: A Please explain
Given answer: APlease explain
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1 votes
2 answers
318
Permutation and Combination
A mint prepares metallic calendars specifying months , dates and days in the form of monthly sheets (one plate for each month ) . how many type of feburary calendars should be prepare to serve all the possibilities in the future year ?
A mint prepares metallic calendars specifying months , dates and days in the form of monthly sheets (one plate for each month ) . how many type of feburary calendars shou...
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3 votes
2 answers
319
Combinatorics
In how many ways 5 blue pens and 6 black pens can be distributed to 6 children? a)97020 b)116424 c)8008 d)672
In how many ways 5 blue pens and 6 black pens can be distributed to 6 children?a)97020b)116424c)8008d)672
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1 votes
2 answers
320
How many possible outcomes are there when 5 similar dices are rolled ?
In this question If I consider first total no of outcomes as 6^5 , then I divided it be 6C5 *5! since there are 5 similar dices so the outcome (1 2 3 4 5 ) will be similar to (5 4 3 2 1) . Now what's wrong with this approach ?
In this question If I consider first total no of outcomes as 6^5 , then I divided it be 6C5 *5! since there are 5 similar dices so the outcome (1 2 3 4 5 ) will be simil...
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