Consider a street that is 5 blocks long, where there is a building of height P[i] on the ith block. If you are standing at the very left end of the street, you will be able to see some of these 5 buildings, but unfortunately many of them will be blocked by a taller building. In this question, consider a random permutation of {1, 2, 3, 4, 5} buildings, where each of the 5! = 5×4×3×2×1 = 120 options is equally likely to occur. Suppose the buildings are placed on the street according to this random permutation. (c) Determine the probability that you will be able to see exactlytwoof the five buildings. (d) Determine the expected value (i.e., average) of the number of buildings you will be able to see.
Consider a street that is 5 blocks long, where there is a building of height P[i] on the ith block.
If you are standing at the very left end of the street, you will be able to see some of these 5 buildings, but unfortunately many of them will be blocked by a taller building.
In this question, consider a random permutation of {1, 2, 3, 4, 5} buildings, where each of the 5! = 5×4×3×2×1 = 120 options is equally likely to occur.
Suppose the buildings are placed on the street according to this random permutation.
(c) Determine the probability that you will be able to see exactlytwoof the five buildings.
(d) Determine the
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