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Consider a permutation of the first n positive integers. For example, if n = 10, then a possible permuta- tion is P = [5, 2, 1, 8, 4, 7, 10, 9, 3, 6]. Consider a street that is 10 blocks long, where there is a building of height Pli] on the ith block. For example, there is a building of height 5 on the first block, a building of height 2 on the second block, a building of height 1 on the third block, and so on. If you are standing at the very left end of the street, you will be able to see some of these 10 build- ings, but unfortunately many of them will be blocked by a taller building. you can only see buildings 5, 8, 10. YOU - OUR BUILDINGS For the permutation above, you will only be able to see three buildings, namely 5, 8, and 10. In this question, consider a random permutation of {1, 2, 3, 4, 5}, where each of the 5! = 5 x 4x 3x 2x 1 = 120 options is equally likely to occur. Suppose the buildings are placed on the street according to this random permutation. (a) Determine the probability that you will only be able to see exactly one of the five buildings. (b) Determine the probability that you will be able to see exactly four of the five buildings. (c) Determine the probability that you will be able to see exactly two of the five buildings. (d) Determine the expected value (i.e., average) of the number of buildings you will be able to see. For each question, you are welcome to write your answer as a fraction or convert it to a decimal number. For full marks, you must clearly and carefully justify each