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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

1 votes
0 answers
302
In an examination, the score in each of the four languages
In an examination, the score in each of the four languages – Bengali, Hindi, Urdu and Telegu- can be integers between 0 and 10. Then the number of ways in which a student can secure a total score of 21 is (A) 880; (B) 760; (C) 450; (D) 1360.
In an examination, the score in each of the four languages – Bengali, Hindi, Urdu and Telegu- can be integers between 0 and 10. Then the number of ways in which a stude...
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0 votes
4 answers
303
What is the number of ways to distribute ten identical sweets to three children?
What is the number of ways to distribute ten identical sweets to three children? If each children gets at least one sweet. If 1 condition is omitted. P.S. I do not know the answer.
What is the number of ways to distribute ten identical sweets to three children?If each children gets at least one sweet.If 1 condition is omitted.P.S. I do not know the ...
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4 votes
2 answers
304
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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0 votes
1 answer
305
Kenneth Rosen Edition 7 Exercise 6.6 Question 5 (Page No. 438)
Find the next larger permutation in lexicographic order after each of these permutations. $1432$ $54123$ $12453$ $45231$ $6714235$ $31528764$
Find the next larger permutation in lexicographic order after each of these permutations.$1432$$54123$$12453$$45231$$6714235$$31528764$
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0 votes
1 answer
306
total possible 4 digit numbers from given 6 digits
total possible 4 digit numbers from 2,3,5,6,7,9 without repetition? total numbers possible less than 500? 360, 130 360, 100 240, 120 none
total possible 4 digit numbers from 2,3,5,6,7,9 without repetition? total numbers possible less than 500?360, 130 360, 100 240, 120 ...
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0 votes
1 answer
307
Kenneth Rosen Edition 7 Exercise 6.5 Question 11 (Page No. 432)
How many ways are there to choose eight coins from a piggy bank containing $100$ identical pennies and $80$ identical nickels?
How many ways are there to choose eight coins from a piggy bank containing $100$ identical pennies and $80$ identical nickels?
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0 votes
1 answer
308
How many bit strings of length n contains at least ,at most , exactly r 1's
How many bit strings of length n contains 1)at least 2) at most 3) exactly r 1's
How many bit strings of length n contains 1)at least 2) at most 3) exactly r 1's
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22 votes
1 answer
309
Recurrence Relation - Self Doubt
What is the recurrence relation for the ternary strings of length $n$ which can be constructed using 0,1 or 2 only such that the number of 0’s and number of 1's is odd ?
What is the recurrence relation for the ternary strings of length $n$ which can be constructed using 0,1 or 2 only such that the number of 0’s and number of 1's is od...
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1 votes
2 answers
311
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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0 votes
1 answer
312
Kenneth Rosen Edition 7 Exercise 6.5 Question 8 (Page No. 432)
How many different ways are there to choose a dozen donuts from the $21$ varieties at a donut shop?
How many different ways are there to choose a dozen donuts from the $21$ varieties at a donut shop?
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1 votes
2 answers
314
combination
How many binary sequences of length 10 are possible with exactly 4 zeros and no two zeros are consecutive?
How many binary sequences of length 10 are possible with exactly 4 zeros and no two zeros are consecutive?
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1 votes
2 answers
316
Kenneth Rosen Edition 7 Exercise 6.5 Question 24 (Page No. 432)
How many ways are there to distribute $15$ distinguishable objects into five distinguishable boxes so that the boxes have one, two, three, four, and five objects in them, respectively.
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2 votes
0 answers
317
Permutations and combinations
A florist sells roses of five different colours. How many bunches of a half dozen roses can be formed?
A florist sells roses of five different colours. How many bunches of a half dozen roses can be formed?
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1 votes
2 answers
319
Sheldon Ross
From 10 married couples, we want to select group of 6 that is not allowed to contain a married couple. How many choices are there?
From 10 married couples, we want to select group of 6 that is not allowed to contain a married couple. How many choices are there?
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1 votes
1 answer
320
combinatory
From a group of 10 professors how many ways can a committee of 5 members can be formed so that atleast one of the professor A and professor B will be included ?
From a group of 10 professors how many ways can a committee of 5 members can be formed so that atleast one of the professor A and professor B will be included ?
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