Last visit was: 21 Nov 2024, 11:02 It is currently 21 Nov 2024, 11:02

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12196 [5]
Given Kudos: 136
Send PM
Most Helpful Community Reply
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12196 [4]
Given Kudos: 136
Send PM
General Discussion
avatar
Intern
Intern
Joined: 08 Jul 2021
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 6
Send PM
Manager
Manager
Joined: 19 Jun 2021
Posts: 52
Own Kudos [?]: 27 [0]
Given Kudos: 24
Send PM
Re: At a dinner party, 6 people (A, B, C, D, E, and F) are to be seated ar [#permalink]
What about the following solution? Does it work, or was I just lucky?

Step 1:
Open the circle to a line.
_ _ _ _ _ _

Step 2:
We know that the 2 of them are constantly relative to each other, and we can use $ for that.
$ _ _ $ _ _

Step 3:
Now we can use basic counting to find the way to put the other 4 people.
4! = 4x3x2x1 = 24


GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
Image

At a dinner party, 6 people (A, B, C, D, E, and F) are to be seated around the circular table shown above. Two seating arrangements are considered different only when the positions of the people are different relative to each other. If person B must sit directly across from person C (e.g., B in chair #1 and C in chair #4), what is the total number of different possible seating arrangements for the group?

(A) 20
(B) 24
(C) 48
(D) 72
(E) 144

Let’s solve this question via the most basic of counting techniques, the Fundamental Counting Principle (FCP):

As always, we’ll begin the most restrictive stage(s):
Stage 1: We can seat person B in 6 ways (seat B in chair 1, 2, 3, 4, 5 or 6).
Stage 2: At this point, we can seat person C in 1 way (directly across from person B).
Stage 3: We can seat person A in 4 ways (any remaining seat that isn’t yet occupied)
Stage 4: We can seat person D in 3 ways (any remaining seat that isn’t yet occupied)
Stage 5: We can seat person E in 2 ways (any remaining seat that isn’t yet occupied)
Stage 6: We can seat person F in 1 way

Now apply the Fundamental Counting Principle to see that the total number of ways to seat all 6 people = (6)(1)(4)(3)(2)(1) = 144

Important: Since two seating arrangements are considered different only when the positions of the people are different relative to each other, we see that we’ve counted each unique outcome 6 times.

For example, these 6 arrangements . . .
Image
. . . are considered 1 unique arrangement because the relative positions of the six people are the same in each case. .

So, to account for counting each arrangement 6 times, we’ll divide 144 by 6 to get 24, which means the correct answer is B.

Answer: B
Verbal Expert
Joined: 18 Apr 2015
Posts: 30001
Own Kudos [?]: 36335 [0]
Given Kudos: 25926
Send PM
Re: At a dinner party, 6 people (A, B, C, D, E, and F) are to be seated ar [#permalink]
Expert Reply
Bump for further discussions
GRE Instructor
Joined: 06 Nov 2023
Posts: 83
Own Kudos [?]: 86 [1]
Given Kudos: 18
Send PM
At a dinner party, 6 people (A, B, C, D, E, and F) are to be seated ar [#permalink]
1
There are just 3 seating positions based on the seating arrangement. Each of the positions will have 2 possibilities therefore number of different seating arrangements = 3 x 8 = 24.


Adewale Fasipe, Lagos Nigeria.
Prep Club for GRE Bot
At a dinner party, 6 people (A, B, C, D, E, and F) are to be seated ar [#permalink]
Moderators:
GRE Instructor
83 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne