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19 silver dollar struck in 1903 there are 8 from Iowa, 7 from Denver and 4...

19 silver dollar struck in 1903 there are 8 from Iowa, 7 from Denver and 4 from Illinois
If 6 are chosen at random find the probability that you get at least 1 from Illinois
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Answer #1

Required probability is

1-\text{probability no dollar from Illinois} =1-{^{15}{C}_{6}\over ^{19}^{C}_{6}}\\ \\~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~=1-{15!(19-6)!\over 19!(15-6)!}\\ \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~=1-0.184468524\\ \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~=0.815531476

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