Eight students (Anna, Brian, Carol, ...) are to be seated around a cir-cular table with eight seats, and two seatings are considered the samearrangement if each student has the same student to their right in bothseatings. (a) How many seatings of the eight students are there? b) How many arrangements of the eight students are there? (c) How many arrangements of the eight students are there with Annasitting next to Brian? (d) How many arrangements of the eight students are there with Briansitting next to both Anna and Carol? (e) How many arrangements of the eight students are there with Briansitting next to either Anna or Carol?

Eight students (Anna, Brian, Carol, ...) are to be seated around a cir-cular table with eight seats, and two seatings are considered the samearrangement if each student has the same student to their right in bothseatings. (a) How many seatings of the eight students are there? b) How many arrangements of the eight students are there? (c) How many arrangements of the eight students are there with Annasitting next to Brian? (d) How many arrangements of the eight students are there with Briansitting next to both Anna and Carol? (e) How many arrangements of the eight students are there with Briansitting next to either Anna or Carol?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

3. Eight students (Anna, Brian, Carol, ...) are to be seated around a cir-cular table with eight seats, and two seatings are considered the samearrangement if each student has the same student to their right in bothseatings.

(a) How many seatings of the eight students are there?

b) How many arrangements of the eight students are there?

(d) How many arrangements of the eight students are there with Briansitting next to both Anna and Carol?

(e) How many arrangements of the eight students are there with Briansitting next to either Anna or Carol?

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Please keep in mind that the order of the students sitting matters so you should use permutation