'2. [30 marks; 15 each part] Twelve mutual fund managers are being evaluated on the basis of historical performance over the last ten years. Six are value managers (looking for companies at low prices relative to earnings potential) and six are growth managers (looking for companies with high earnings growth). Within each set, there is an ordering of experience, {V1, V2, .. . V5} and {G1, G2, . . . G5}, with subscript 1 indicating the most experienced, and 6 the least. (This ranking information is all that we have concerning experience; we don't have exact number of years.) Assume for this question that the market is perfectly efcient: that is, all infor- mation useful in predicting future returns is embodied in the stock price, so that no information these managers possess is of any use, and the ordering that emerges is a purely random one. All twelve are ranked. What is the probability that: - -the top three managers in the ranking all turn out to be value managers; - the top three managers turn out to be ranked in order of experience, regardless of style (ie regardless of value or growth investing). That is, the subscript 0f the rst ranked manager is strictly less than that of the second-ranked, and the subscript of the secondranked is strictly less than that of the third ranked