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.
The probability of a person sitting in a specific position in a circle depends on the total number of people in the circle and the number of positions available. For example, if there are 10 people in the circle and 10 positions available, the probability of a person sitting in a specific position is 1/10 or 10%.
The number of people in a circle directly affects the probability of a person sitting in a certain position. As the number of people increases, the total number of positions available decreases, therefore decreasing the probability of a person sitting in a specific position.
Yes, the shape of the circle can affect the probability of a person sitting in a certain position. For example, if the circle is a regular polygon with an even number of sides, the probability of a person sitting in the center position is higher compared to a circle with an odd number of sides.
The position of the first person chosen does not affect the probability of the other people sitting in a circle. The probability remains the same regardless of the initial position chosen.
Yes, the probability of a person sitting in a circle can be calculated using the formula P = 1/n, where P is the probability and n is the total number of positions available in the circle. However, this formula assumes that all positions are equally likely to be chosen.