5.4-5 What is the probability that a k-string over a set of size n forms a k-permutation? How does this question relate to the birthday paradox? k-permuation over set n is $_n\mathrm{P}_k$ we can construct k-length over set n of size by $$n.n.n...n = n^k$$ the probability is $_n\mathrm{P}_k/n^k$ $$n(n-1)(n-2)...1/n^k (n-k)!$$ $$(n-1)(n-2)...(n-k+1)/n^{k-1} $$ The above equation looks similar to the probability of distinct birthdays k people in a room can have. Where k is the no of people and n -s no of days in a year.
Tuesday, January 1, 2013
5.4-5
5.4-5 What is the probability that a k-string over a set of size n forms a k-permutation? How does this question relate to the birthday paradox? k-permuation over set n is $_n\mathrm{P}_k$ we can construct k-length over set n of size by $$n.n.n...n = n^k$$ the probability is $_n\mathrm{P}_k/n^k$ $$n(n-1)(n-2)...1/n^k (n-k)!$$ $$(n-1)(n-2)...(n-k+1)/n^{k-1} $$ The above equation looks similar to the probability of distinct birthdays k people in a room can have. Where k is the no of people and n -s no of days in a year.
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