Unformatted text preview: in ± 5 2 ² ways. To Fll the remaining three digit location can be done in 8 · 7 · 6 ways. This gives in total 9 · ± 5 2 ² · 8 · 7 · 6 = 30240 . Lets now count the number Fve digit numbers with two repeated digits. To compute this we might argue as follows. We can select the Frst digit and its location in 9 · ± 5 2 ² ways. We can select the second repeated digit and its location in 8 · ± 3 2 ² ways. The Fnal digit can be selected in seven ways, giving in total 9 ± 5 2 ² · 8 ± 3 2 ² · 7 = 15120 . We note, however, that this analysis (as it stands) double counts the true number of Fve digits numbers with two repeated digits. This is because in Frst selecting the Frst digit from...
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 Winter '08
 G.JOGESHBABU
 Probability, Numerical digit, digit, ﬁve digit numbers

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