2. Following the legend of Merlin and King Arthur, a corporate CEO creates a rou

Question

2. Following the legend of Merlin and King Arthur, a corporate CEO creates a round table for himself and his board of 11 directors so that no one, not even himself, would occupy a chair more enviable than another. That's the theory. In practice, we know that while the particular chair is not important, seating order (who sits next to whom) is important - those next to the CEO could more easily gain his favor than those far away. (a) Assuming a seat for CEO and each of his 11 directors (12 seats total), how many seating config- urations are possible? (b) Assuming random seating, what is the chance that the CEO finds himself seated between his favorite (Sally) and least favorite (Bob) directors?

Explanation / Answer

Number of permutations = n-1 ! = 12-1 ! = 11!

There are 39916800 ways of sitting.

b) Let us assume that Sally,CEO,Bob are one object

No. of ways = 10-1! = 9!

There are two ways in whcih sally and Bob can be arranged( left or right)

Hence, probability = 9! * 2/ 11! = 2/110

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