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Unformatted text preview: , i = 1 ,...k, to be the event that the i-th member of the ﬁxed set picks her/his own hat. Then, describing event E in terms of the G i , i = 1 ,...k , we have that P ( E ) = = , using the multiplication rule, = , evaluating each term, = . 3. Next, we want to calculate P ( F | E ), or in words, P ( F | E ) = P ( ) = , using ( * ), since the remaining ( N-k ) graduates are choosing from among their own ( N-k ) hats. 4. So, for the ﬁxed set of k graduates, the probability that we wish to calculate is P ( EF ) = . 5. Accounting for the number of ways we could have chosen the ﬁxed set of k graduates, this gives us the overall answer of P (exactly k matches) = , = ....
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