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Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
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Recent questions tagged counting
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1
PGEE 2019
for(int i=0; i<=100;i++) { if (i % 3 == 0) printf("Great); if(i%5 == 0) printf("India"); } Count the number of times GreatIndia is printed. 6 20 33 none of these
asked
Apr 29
in
Programming
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manikgupta123
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115
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177
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iiithpgee
loop
counting
programming
+1
vote
3
answers
2
Turing Machine Self Doubt
Can someone explain in details how set of all TM is countable?
asked
Mar 23
in
Theory of Computation
by
aditi19
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3.5k
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56
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turingmachine
theoryofcomputation
counting
settheory
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1
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3
Self Doubt
From a group of 5 woman and 7 man we have to select a committee consisting of 2 woman and 3 men. Find the total number of ways to select such committed if (1 and 2 are a separate question) 1. Four man refuse to be in the same committee 2. 2 woman refuse to be in the same committee.
asked
Feb 8
in
Combinatory
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smsubham
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9.3k
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67
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counting
permutationsandcombinations
discretemathematic
discretemathematics
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0
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4
indistinguishable objects distinguishable boxes
how to know when to apply which case for : indistinguishable object indistinguishable boxes. Example 12 balls are distributed at random among three boxes.The probability that the first box will contain three balls is_____. Example  number of ways we can arrange 5 books in 3 shelves.
asked
Jan 25
in
Mathematical Logic
by
bts1jimin
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283
points)

38
views
counting
0
votes
0
answers
5
MadeEasy Full Length Test 2018: Graph Theory  Counting
The Number of Labelled possible graph given below ? what I did was → we doesn't remove any of the edge out of 4 = $\binom{4}{0}$ [Because a Graph is subgraph of itself] we can remove any of one edge out of 4 = $\binom{4}{1}$ we can remove any ... out of 4 = $\binom{4}{2}$ similarly , $\binom{4}{3}$ , $\binom{4}{4 }$ then , add of the them
asked
Jan 15
in
Graph Theory
by
Magma
Boss
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13.8k
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88
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graphtheory
discretemathematics
counting
madeeasytestseries2019
madeeasytestseries
0
votes
1
answer
6
Kenneth Rosen Edition 6th Exercise 6.1 Example 7 (Page No. 399)
this is an example taken from Rosen. but I’m unable to understand to understand the solution given there can someone pls explain me in details
asked
Dec 10, 2018
in
Combinatory
by
aditi19
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3.5k
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54
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kennethrosen
discretemathematics
#recurrencerelations
counting
0
votes
1
answer
7
Zeal Test Series 2019: Graph Theory  Counting
Is there any short trick to do it ?
asked
Nov 17, 2018
in
Graph Theory
by
Prince Sindhiya
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6.3k
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107
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zeal
graphtheory
counting
zeal2019
0
votes
1
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8
Number of substrings for a given sub string having repeated symbols
Lets for a a given string aabbbccdd I need to find the number of substrings possible how to go about it? Does the n(n+1)/2 formula work here also?
asked
Nov 5, 2018
in
Theory of Computation
by
sripo
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2.6k
points)

124
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permutationsandcombinations
counting
theoryofcomputation
algorithms
finiteautomata
0
votes
1
answer
9
RosenPigeonhole Principle
How many cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds? what this question means?
asked
Oct 25, 2018
in
Combinatory
by
aditi19
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3.5k
points)

99
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pigeonholeprinciple
permutationsandcombinations
counting
discretemathematics
+1
vote
1
answer
10
Counting
A number of ways we can arrange letters of the word " TESTBOOK " such that E always comes between O's is ___________
asked
Oct 24, 2018
in
Combinatory
by
Lakshman Patel RJIT
Boss
(
36.3k
points)

91
views
discretemathematics
permutationsandcombinations
counting
+1
vote
0
answers
11
Combinations
In how many ways a team of 11 players be selected from 14 players when two of them can play as goalkeepers only?
asked
Oct 24, 2018
in
Mathematical Logic
by
Vaishnavi01
(
217
points)

40
views
permutationsandcombinations
counting
0
votes
0
answers
12
cormen 7th edition counting
How many ways are there for a horse race with three horses to finish if ties are possible?(Note: Two or three horses may tie) My answer is 9 but correct answer is 13. In the solution they have even considered the case of all three horses tying ... is it possible that in 3 horses race all three tie at third position? How can we get third without getting first and second?
asked
Oct 5, 2018
in
Combinatory
by
sushmita
Boss
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17.1k
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38
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permutationsandcombinations
discretemathematics
counting
0
votes
0
answers
13
Counting
1)In how many ways we can put n distinct balls in k identical bins? 2)In how many ways we can put n distinct balls in k identical bins such that no bin is empty?
asked
Sep 15, 2018
in
Probability
by
srestha
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114k
points)

79
views
discretemathematics
counting
0
votes
2
answers
14
PigeonHole Principal
A drawer contains a dozen of brown and dozen of black socks,all unmatched.A man takes socks out at random in the dark. How many socks must he take out to be sure that he has atleast two black socks ?
asked
Sep 3, 2018
in
Mathematical Logic
by
Na462
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8.7k
points)

82
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pigeonholeprinciple
permutationsandcombinations
counting
+2
votes
1
answer
15
MADEEASY
Consider a set S={1000,1001,1002........,9999}. The numbers in set S having atleast one digit as 2 and atleast one digit as 5 are?
asked
Jul 29, 2018
in
Combinatory
by
Utkarsh Joshi
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7.6k
points)

217
views
counting
+1
vote
0
answers
16
Testbook Test Series: Graph Theory  Counting
asked
Jul 15, 2018
in
Graph Theory
by
Bhagyashree Mukherje
Active
(
2.6k
points)

66
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testbooktestseries
graphtheory
counting
+1
vote
0
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17
Combinatorics Question on Bit Strings
How many bit strings of length 8 contain either three consecutive 0's or four consecutive 1's ? MY APPROACH : Initially, for 3 consecutive 0's: 000_ _ _ _ _ =>2^5 = 32 WAYS 1000_ _ _ _ =>2^4 = 16 WAYS _1000_ _ _ =>2^4 = 16 WAYS _ _1000_ ... =>2*3! = 12 WAYS so, total ways = 112 + 48  12 = 148 ways But answer is given as 147 ways. Where am I wrong?
asked
Jul 6, 2018
in
Combinatory
by
Balaji Jegan
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5.4k
points)

100
views
permutationsandcombinations
counting
discretemathematics
+1
vote
1
answer
18
Kenneth Rosen Edition 6th Exercise 5.6 Example 5 (Page No. 385)
I am not getting this condition. Can someone please explain that condition with that example.
asked
Jul 5, 2018
in
Combinatory
by
tusharp
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6.5k
points)

75
views
discretemathematics
kennethrosen
counting
+3
votes
1
answer
19
Kenneth Rosen Edition 6th Exercise 6.4 Question 6 e (Page No. 440)
nC2 for n=0,1,2,3...
asked
Jun 14, 2018
in
Mathematical Logic
by
sunil sarode
Active
(
1.5k
points)

132
views
kennethrosen
discretemathematics
counting
generatingfunctions
0
votes
1
answer
20
Combinatorics
Among the integers $1,2,3,....,200$ if $101$ integers are chosen,then show that there are two among the chosen,such that one is divisible by the other.
asked
May 29, 2018
in
Mathematical Logic
by
Sammohan Ganguly
(
475
points)

144
views
engineeringmathematics
discretemathematics
permutationsandcombinations
pigeonholeprinciple
counting
+2
votes
2
answers
21
Ace booklet
How many ways $4$ boys and $4$ girls can sit in a row so that no two girl are sitting side by side
asked
May 29, 2018
in
Mathematical Logic
by
Rahul singh dhakrey
(
43
points)

97
views
engineeringmathematics
permutationsandcombinations
counting
discretemathematics
0
votes
1
answer
22
Combinatorics
Given m integers $a_1,a_2,....,a_m$ show that there exist integers $k,s$ with $0 \leq k < s \leq m$ such that $a_{k+1} + a_{k+2} + .....+a_s$ is divisible by $m$.
asked
May 29, 2018
in
Mathematical Logic
by
Sammohan Ganguly
(
475
points)

68
views
engineeringmathematics
discretemathematics
permutationsandcombinations
pigeonholeprinciple
counting
+1
vote
1
answer
23
Pigeonhole Principle (2)
Suppose a graph $G$ has $6$ nodes. Prove that either $G$ or $G'$ must contain a triangle. ($G'$ is the complement of $G$.) Prove it using pigeonhole principle.
asked
May 25, 2018
in
Combinatory
by
Sammohan Ganguly
(
475
points)

68
views
pigeonholeprinciple
permutationsandcombinations
counting
0
votes
1
answer
24
Combinatorics
Find the number of seven digit integers with sum of the digits equal to $11$ and formed by using the digits $1,2$ and $3$ only. Soln $X_{1}+X_{2}+.......X_{7}=11$ $(x+x^{2}+x^{3})^{7}$ $(x(1+x+x^{2}))^{7}$ $x^{7}(1+x+x^{2})^{7}$ ... (7k) (x)3k) * ((7+k1k) xk) $((\binom{7}{k}) (x)^{3k}) \times (\binom{7+k1}{k} x^{k})$ Now not able to proceed. Kindly help.
asked
May 23, 2018
in
Combinatory
by
mbisht
(
275
points)

83
views
engineeringmathematics
generatingfunctions
discretemathematics
counting
+4
votes
1
answer
25
Kenneth Rosen Edition 6th Exercise 5.3 Question 24 (Page No. 361)
How many ways are there to arrange $6$ Men and $10$ Women in a row such that no two men are together. This can simply be answered by putting $10$ women first which gives $11$ ... Why the both answers are not same. What am I missing? Which approach is correct?
asked
Apr 30, 2018
in
Combinatory
by
surajumang08
(
199
points)

128
views
kennethrosen
discretemathematics
counting
permutationsandcombinations
+2
votes
4
answers
26
Counting
Show that, in a grid, the number of paths from $(0,0)$ to $(n,n)$ which does not cross ( it could touch ) the line $x = y$ is \begin{align*} \frac{1}{1+n}\binom{2\cdot n}{n} = \binom{2\cdot n}{n}  \binom{2\cdot n}{n1} \end{align*} After that, show the number of balanced paranthesis strings of length $2n$ is same as the above result.
asked
Apr 27, 2018
in
Set Theory & Algebra
by
Debashish Deka
Veteran
(
58k
points)

118
views
counting
combinatoricsiitb
0
votes
2
answers
27
ISISAMPLE6
A club with $x$ members is organized into four committees such that, each member is in exactly two committees, any two committees have exactly one member in common. Then $x$ has exactly two values both between $4$ and $8$ exactly one value and this lies between $4$ and $8$ exactly two values both between $8$ and $16$ exactly one value and this lies between $8$ and $16$
asked
Mar 23, 2018
in
Mathematical Logic
by
jjayantamahata
Active
(
1.8k
points)

64
views
counting
+1
vote
2
answers
28
Kenneth Rosen Edition 6th Exercise 5.5 Question 35 (Page No. 380)
How many strings with seven or more characters can be formed from the letters of the word $\text{EVERGREEN}$ ?
asked
Mar 22, 2018
in
Combinatory
by
Abhinavg
Junior
(
501
points)

328
views
discretemathematics
kennethrosen
counting
permutationsandcombinations
+4
votes
1
answer
29
Discrete Mathematics By Kenneth H Rosen Counting
One Hundred tickets, numbered $1,2,3,...,100$, are sold $100$ different people for a drawing. Four different prizes are awarded, including a grand prize(a trip to Tahiti).How many ways are there to award the prizes if the people holding tickets $19$ and $47$ both win prizes? the people holding tickets $19,47,$ and $73$ all win prizes?
asked
Mar 20, 2018
in
Combinatory
by
Sayed Athar
(
103
points)

159
views
discretemathematics
permutationsandcombinations
counting
+2
votes
0
answers
30
Number of unique solution
Suppose there is an equation $x_{1}+x_{2}+...........x_{r}=n$ Then number of unique solution in this given equation?
asked
Mar 13, 2018
in
Combinatory
by
srestha
Veteran
(
114k
points)

86
views
counting
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