Recent questions in Discrete Mathematics

Recent questions in Discrete Mathematics

0 votes

1 answer

1

Degree sequence of graph
Someone please solve it.

GateOverflow04 asked in Graph Theory 6 days ago

by GateOverflow04

30 views

0 votes

1 answer

2

Doubt:
Let “m” be the number of edges, “n” the number of vertices and “k” the number of connected components of a graph G. Prove that: $\left ( n-k \right )\leq m\leq \frac{\left ( n-k \right )\left ( n-k+1 \right )}{2}$ Why least number of edges are $\left ( n-k \right )$ and Why most number of edges are $\frac{\left ( n-k \right )\left ( n-k+1 \right )}{2}$ ? What is the idea behind this prove?

Simmi Kaur asked in Graph Theory Jun 28

36 views

3 votes

2 answers

3

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 1
How many words can be formed by re-arranging the letters of the word “PROBLEMS” such that $P$ and $S$ occupy the first and last position respectively? (Note: The words thus formed need not be meaningful)

GO Classes asked in Combinatory Jun 14

121 views

4 votes

1 answer

4

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 2
A set of cards is numbered $1$ through $6.$ Quantity A: The number of ways to pick $3$ of the $6$ cards such that card number $1$ ... Quantity B is greater than Quantity A. The two quantities are equal. The relationship cannot be determined from the information given.

GO Classes asked in Combinatory Jun 14

101 views

4 votes

2 answers

5

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

GO Classes asked in Combinatory Jun 14

82 views

3 votes

1 answer

6

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 4
We go to a pizza party, and there are $5$ types of pizza. We have been starving for days, so we can eat $13$ slices, but we want to sample each type at least once. In how many ways can we do this? Order does not matter.

GO Classes asked in Combinatory Jun 14

97 views

3 votes

1 answer

7

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 5
How many integer solutions does the equation $ x_{1}+x_{2}+x_{3}+x_{4}=15 $ have, if we require that $x_{1} \geq 2, x_{2} \geq 3, x_{3} \geq 10$ and $x_{4} \geq-3 ?$

GO Classes asked in Combinatory Jun 14

61 views

4 votes

1 answer

8

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 6
How many integer solutions are there to the system of inequalities $ x_{1}+x_{2}+x_{3}+x_{4} \leq 15, \quad x_{1}, \ldots, x_{4} \geq 0 ? $

GO Classes asked in Combinatory Jun 14

73 views

5 votes

3 answers

9

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 7
We want those bit strings of length $10$ which Start and end with the symbol $1.$ No two zeroes are consecutive. How many such bit strings are there?

GO Classes asked in Combinatory Jun 14

195 views

3 votes

1 answer

10

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 8
How many ways are there to split a dozen people into $3$ teams, where one team has $2$ people, and the other two teams have $5$ people each?

GO Classes asked in Combinatory Jun 14

101 views

6 votes

1 answer

11

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 9
A student is given an exam consisting of $8$ essay questions divided into $4$ groups of $2$ questions each. The student is required to select a set of $6$ questions to answer, including at least $1$ question from each of the $4$ groups. How many sets of questions satisfy this requirement?

GO Classes asked in Combinatory Jun 14

197 views

5 votes

1 answer

12

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 10
In how many rearrangements of the letters of the word SCINTILLATING will no two 'I's appear together? ${ }^{11} \mathrm{C}_{3} * 13!$ $\frac{10 !}{2 ! * 2 ! * 2 !}$ ${ }^{11} \mathrm{C}_{3} * 3 ! * 10 !$ ${ }^{11} \mathrm{C}_{3} \frac{10 !}{2 ! * 2 ! * 2 !}$

GO Classes asked in Combinatory Jun 14

93 views

3 votes

2 answers

13

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 11
How many squares are there in a chess board? $64$ $204$ $1296$ $4096$

GO Classes asked in Combinatory Jun 14

149 views

2 votes

1 answer

14

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 12
How many rectangles are there in a chess board?

GO Classes asked in Combinatory Jun 14

72 views

2 votes

1 answer

15

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 13
For which of the following events will the number of outcomes exceed $50?$(Indicate all such events.) The number of outcomes in which at least three heads appear in $6$ consecutive tosses of a fair coin. ... number of outcomes in which all the vowels appear together when the letters of the word 'PRIORITY' are reordered.

GO Classes asked in Combinatory Jun 14

56 views

2 votes

2 answers

16

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?

GO Classes asked in Combinatory Jun 14

69 views

2 votes

1 answer

17

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 15
In an examination, a question paper consists of $12$ questions divided into two parts i.e, Part I and Part II, containing $5$ and $7$ questions respectively. A student is required to attempt $8$ questions in all, selecting at least $3$ from each part. In how many ways can a student select the questions?

GO Classes asked in Combinatory Jun 14

74 views

6 votes

1 answer

18

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 16
Count the number of non-negative integer solutions to $ 3 x_{1}+3 x_{2}+3 x_{3}+7 x_{4}=22 . $

GO Classes asked in Combinatory Jun 14

132 views

2 votes

1 answer

19

no of solutions to the following inequality 12 <= w + x + y + z <= 14
No. of solutions to the following inequality 12 <= w + x + y + z <= 14 where w,x,y,z>=0

khushitshah asked in Combinatory Jun 8

72 views

0 votes

1 answer

20

Can someone please explain how "I am lying" is a Liars paradox? and how the truth values are toggling here?

Roy12 asked in Mathematical Logic Jun 8

by Roy12

55 views

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