Question

2. A group of 24 physical doctors from three countries consists of 7 Americans, 8 British and 9 Chinese. They (wearing masks) are seated at random around a (large enough) table to discuss the means of treatment of COVID-19 patients. Compute the following probabilities: (a) that all the Americans sit together; (b) that all the Americans and the British sit together; (c) that all the Americans, all the British and all the Chinese sit together.

3. Randomly choose 6 doctors from the group of doctors in the above question to evaluate the efficiency of one type of treatment of COVID-19. It is unfair if all of the 6 doctors are from the same country. What is the probability that the selection is fair?

Answer 1

2)

a) Probability that all americans sit together = (18!*7!)/24!

b) Probability that all americans and the british sit together = (10!*15!)/24!

Probability that all americans sit together and all british sit together = (7!*8!*11!)/24!

c)Probability that all americans sit together ,all british and all chinese sit together = (7!*8!*9!*3!)/24!

3) the probability that the selection is unfair =  Probability of selecting 6 amercians + Probability of selecting 6 cinese + Probability of selecting 6 british

  

therefore probability that the selection is fair = 1- probability of unfair