Question

Show that if n people go to a party and some shake hands with others but not with themselves, then there are two people who have shaken hands with the same number of people.

Answer #1

******Your honest feedback is very important for better
results******

**Thanks**

Show that if n people go to a party and some shake hands with
others but not with themselves, then there are two people who have
shaken hands with the same number of people.(use graph theory)

1/ Imagine a party with n people. When a person comes to
the party they go and shake hands with a few other people (but not
necessarily everyone - in fact there can be unfriendly people who
do not shake hands with anyone!). None of the attendees
narcissistic enough to shake hands with themselves. Prove that
there are two people who shake the same number of
hands.
For example, suppose 3 people attend the party and everyone
shakes hand with...

suppose Alice, Bob, Carol Dave and Eden attend a party.
Alice shakes hand with Bob, Carol and Eden; Bob shakes hand with
Alice and Dave; Carol shakes hand with Alice and Dave; Dave shakes
hand with Bob and Carol; Eden shakes hand with Alice
1) represent the above scenario as a graph and define
your notation is this graph cyclic or acyclic, directed or
undirected?
2) find the degrees of each vertex in your graph are
there two vertexes that...

For n > 2, suppose that there are n people at a party and
each of these people shake hands (exactly one
time) with all of the other there (and no one shakes hands with
himself or herself). Find the total number
of hand shakes by solving a non-homogeneous recurrence
relation.

There are n distinct recruiters at a recruiting event. Every
second one of the n recruiters uniformly at random comes by to
shake your hand, and then walks back. The same recruiter may come
to shake your hand multiple times. However, by the kth recruiter (k
∈ Z +), you need to leave the event. At this point (after k
seconds), what is the expected number of recruiters you' have not
shaken hands with?

Prove that if there are n≥2 people at a party, then at least 2
of them have the same number of
friends at the party.
(Hint: The Pigeonhole Principle states that if n items are
placed inmcontainers, wheren>m, at
least one container must contain more than one item. You may use
this without proof.)

10 couples go to a party (So 20 people in total). Each of the 20
people are randomly seated at a large round table with 20 chairs.
Let Xi = 1, for i = 1, 2, . . . , 20, if the i th person
is sitting next to the other person in their couple, and 0
otherwise. Let Y be the total number of people who are seated next
to their partner. (Note that the Xi ’s all...

PLEASE WRITE CLEARLY AND SHOW ALL WORK. THANKS
Problem 5 [20 pts]: n people attend a party and each shakes
hands with every other person. Prove, by the method of mathematical
induction that the total number of handshakes is n(n−1) 2 .

There are 6 people at a party. What is the probability that
exactly four people in the party will have the same birthday? (No
restrictions on the other two people, Match the day, i.e. N=365;
derive a formula, no calculations)

Prove by induction
that, if everyone in a group of n people shakes hands, the
number of handshakes is (n-1)n/2.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 35 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago