2022/4/28 21:25 HW #11 (SP22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
HW #11 (SP22)
截止时间 4月21日 23:59 得分 71 问题 16
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最新 尝试 1 9,086 分钟 11，满分 71 分 *
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此测验的分数: 11，满分 71 分 * 提交时间 4月21日 23:59 此尝试进行了 9,086 分钟。
(a) How many edges are there in a graph with 10 vertices, each having a degree 3?
(b) How many edges are there in a graph with 8 vertices, having a degree 1,1,2,2,3,3,3,3 respectively?
(c) How many vertices are there in a graph with 19 edges, having 3 vertices of degree 4 and all the other vertices are of degree 2?
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2022/4/28 21:25 HW #11 (SP22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
How many words can be made from the word “DOCTOR” using all the alphabets with repetition and
without repetition respectively?
repetition: 6*5*4*3*2*1= 720 without repetition: N(o)=2 6!/2=720/2 =360
wrong answer with repetition
In how many ways can the letters of the word PERMUTATIONS be arranged if the
(a) words start with P and end with S
(b) vowels are all together
(c) there are always 4 letters between P and S
a) 10!/2!=1814400 b)5!*(5!/2!)= 2419200 c)14*(10!/2!)= 25401600
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2022/4/28 21:25 HW #11 (SP22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Out of 2 Women and 5 Men, a committee of 3 is to be formed. In how many ways can it be formed if
at least one woman is to be included?
1W 2M or 2W 1M
2C1*5C2+2C2 *5C1 = 2!*(5!/2!3!)+5!/4!= 25
In an examination there are three multiple choice questions and each question has 4 choices. Find the
number of ways in which a student can fail to get all answer correct.
Is the given graph Bipartite?
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2022/4/28 21:25 HW #11 (SP22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Given a graph K and G, Find the complement of graph G. K=
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2022/4/28 21:25 HW #11 (SP22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
You can draw the graph or you can represent the complement graph by the following presentation G= (V, E)
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2022/4/28 21:25 HW #11 (SP22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
By using the Binomial Theorem, the expansion of is (Show your work):
How many solutions are there to the equation
where are non-negative
integers such that ?
Suppose we have a complete graph with 17 vertices, what is the sum of the degrees of all vertices for this graph:
Suppose we have an undirected complete bipartite graph with 22 vertices, what is the maximum number of edges that could exist in this
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2022/4/28 21:25 HW #11 (SP22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Suppose we have a complete graph with 13 vertices, what is the sum of the degrees of all vertices for this graph:
Suppose we have an undirected complete bipartite graph with 18 vertices, what is the maximum number of edges that could exist in this
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答案 2: 您将此项留空
In a small class of 9 students, everyone was asked how many of their friends are also taking the class. Friendship is mutual. Is the following outcome possible: 6, 6, 5, 4, 4, 3, 2, 2, 1?
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2022/4/28 21:25 HW #11 (SP22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
Which of the following is not a subgraph of this graph?
{(1,3), (3,2), (5,8), (3,6), (9,7)} {(0,4), (3,2), (5,8), (3,6), (9,7)} {(1,7), (3,2), (5,8), (5,6), (9,7)} {(1,7), (3,2), (5,8), (3,6), (9,7)}
No, because the sum of the friends given is odd
No, because the number of edges in this graph is odd No, because the sum of the edges is not divisible by 9
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2022/4/28 21:25 HW #11 (SP22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
A Professor needs to select 5 puzzles for the class quiz from a question bank containing 20 questions. How many ways are there?
Find the number of integers between 1 and 10, 000 inclusive which are divisible by
at least one of 3, 5, 7, 11. Hint:
|A ∪ B ∪ C ∪ D| = |A| + |B| + |C| + |D| − |A ∩ B| −
|A ∩ C| − |A ∩ D| − |B ∩ C| − |B ∩ D| −
|C ∩ D| + |A ∩ B ∩ C| + |A ∩ B ∩ D| + |A ∩ C ∩ D| + |B − |A ∩ B ∩ C ∩ D|
A group of friends goes to a movie theatre to watch some movies. They found that there are 8 movies which they found interesting but they have money to watch only 3 of them. If they cannot watch “Fast & the Furious Part-2” unless they watch the Part-1, then, in how many ways can they watch exactly 3 movies?
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2022/4/28 21:25 HW #11 (SP22): CMPSC 360 SP 22, Section 01: Discrete Math/Cs
测验分数: 11，满分 71 分
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