The problem involves arranging a committee of 3 teachers and 4 parents around a round table with 7 seats labeled A to G. Participants are exploring different scenarios for seating arrangements, including cases with and without restrictions.
The discussion includes various interpretations of how to approach the arrangement problem, with some participants questioning the validity of certain calculations and suggesting alternative methods for counting arrangements. There is an ongoing exploration of how to treat the teachers as a single entity versus separate individuals.
Participants are working under the constraints of a round table arrangement, which affects the counting of distinct seating arrangements. There is also a focus on the implications of treating groups as blocks versus individuals in the arrangement process.
desmond iking said:Homework Statement
there are 7 seats around a round table, and is labelled form A to G. Find the number of ways a committee of 3 teachers and 4 parents can sit around the table?
(i ) there is no restriction
my ans is 7!=5040
(ii) all teachers must sit together
the ans is 1008. can someone explain part ii please? my wokring is (6!/(3! x 4!) ) x 4! = 120...
Homework Equations
The Attempt at a Solution
Guessing here, but I think what you mean is that having fixed the order of the 3 teachers you treat them as a single entity. So now you have four parents and a block of teachers.desmond iking said:sorry my working should be 3! x 5! = 720 which means i arrange the teacher in 3 ! ways first , then i arrange the whole set of teacher into another 5! ways.