Question

In the annual picnic for STA 201 course teachers, 11 faculties (including a pair of twins, ) have been selected for a game of musical chair. (A game where all the participants have to sit on chairs arranged in circular fashion). a. How many ways can all those 11 faculties be arranged at the beginning of the game of musical chair? b. If the pair of twins are determined about not sitting beside each other in the first round, how many ways can they sit so that they do not have to sit on adjacent chairs? c. What is the probability that the pair of twins will not be adjacent to each other? [Hint: Probability of an event A, P (A) = No.of outcomes (ways) under event A Total no of possible outcomes ] d. After 5 teachers being eliminated from the game, in how many ways can the remaining teachers be arranged in circular fashion?

Answer 1

Answer:

a) 10!

b) 10! - (9!*2)

c) {10!-(9!*2)} / 10!

d) 11^6

Step-by-step explanation:

For question a, we will follow the (n-1)! formula as it's a circular fashion.

For question b, we will simply minus the possible ways of them sitting together. Which is (9!*2), we can consider both of them as 1. After that following the (n-1)! formula will give us 9!. Now the pair of twins can exchange their chairs in 2 ways. For which we have to multiply it with 2.

For question c, just follow the hint..and we get the answer.

For question d, we will foloow the n^r formula, where n is the number of seats and r is the number of people (Not sure if this same formula works in circular fashion too).

Hope this helps.