Consider a permutation of the first n positive integers. For example, if n = 10, then a possible permutation 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 P[i] 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 buildings, but unfortunately many of them will be blocked by a taller building. For the permutation above, you will only be able to see three buildings, namely 5, 8, and 10. For the following question, assume we have 6 buildings numbered 1 to 6, with the building number equal the height of this building. Ex: building 1 has height 1, building 2 has height 2, etc... Consider a random permutation of {1,2,3,4,5,6}, where each of the 6! options is equally likely to occur. Suppose the buildings are placed on the street according to this random permutation. Determine the probability that you will be able to see exactly two of the six buildings.
Consider a permutation of the first n positive integers. For example, if n = 10, then a possible
permutation 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 P[i] 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 buildings, but unfortunately many of them will be blocked by a taller building.
For the permutation above, you will only be able to see three buildings, namely 5, 8, and 10.
For the following question, assume we have 6 buildings numbered 1 to 6, with the building number equal the height of this building. Ex: building 1 has height 1, building 2 has height 2, etc... Consider a random permutation of {1,2,3,4,5,6}, where each of the 6! options is equally likely to occur. Suppose the buildings are placed on the street according to this random permutation.
Determine the probability that you will be able to see exactly two of the six buildings.
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