Question

In how many ways can 12 party guests be seated around a circular table? What if two people want to sit directly next to each other?

Answer #1

If 12 persons are arranged in a linear way, there are 12! ways to do so. But when it come to a circular arrangement, total number of arrangements = 12!/12=11!.=39976800

If two people want to sit directly next to each other then we consider they are one unit, therefore 11 units are arranged in a circular table.Therfore total arrangement is= 10!*2

Here multiple 2 due to the two people want to sit directly next to each other can interchange between them.

Therefore after sitting two people directly next to each other

Then number of arrangements is=10!*2=7257600.

Its probability is= 0.18154.

Question:
How many ways may 4 males and 4 females be seated around a
circular table if we must have alternating gender (male, female,
male, female etc) and two individuals (lets call them Betty
and Jim) must not be seated next to each other?
Note: As an additional part to this question you are
required to produce a diagram explaining your working or a detailed
description as to why your answer is the only answer. Students
often have difficulty with...

Question:
How many ways may 4 males and 4 females be seated around a
circular table if we must have alternating gender (male, female,
male, female etc) and two individuals (lets call them Betty
and Jim) must not be seated next to each other?
Note: As an additional part to this question you are
required to produce a diagram explaining your working or a detailed
description as to why your answer is the only answer. Students
often have difficulty with...

Six
married couples (twelve people in total) are to be seated around a
circular table. Since the table is circular, two seating
arrangements are considered the same if one is a rotation of the
other. If each of the twelve people randomly chooses a seat, what
is the probability that each member of a married couple sits next
to the other member?

How many ways can 6 people sit around two tables if at least one
person sits around each table?

Circular Permutations and Permutations with Similar Elements
1) In how many ways can three people be made to sit at a round
table?
2) In how many ways can three couples be seated at a round
table, so that men and women sit alternately?
3) In how many ways can five keys be put on a key ring?
4) Find the number of different permutations of the letters of
the word MATHEMATICS.
5) How many different ways can three pennies,...

in how many ways can six people, a,b,c,d,e and f, be
seated in a row such that a and b must sit together and c and d
must never sit together?

60 wedding guests are to be seated at 10 circular tables, each
with 6 seats. Two seating arrangements are considered the same if
the person to the left of each person is unchanged. How many
seating arrangements are possible, and why?

In how many ways can 8 people sit down in a row of 8 chairs? a)
without any restriction b) two specific people will not sit next to
each other. c) the probability that those 2 persons end up next to
each other.

How many ways can n student, n teacher and n parent be arranged
along a table of size 3n if they must be seated alternately and the
first seat (from the left) be allotted to a teacher?
Observe that the alternate seating requirement essentially means
that any 3 consecutive seats must have all different people seated
in them.

In how many ways can 4 friends sit in a row of 12 seats so there
is at least one empty seat between any two friends?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 25 minutes ago

asked 33 minutes ago

asked 35 minutes ago

asked 37 minutes ago

asked 51 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago