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How many ways are there to ride eight of the coasters if order is not important?

12,870 ways

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Oregon State University

Harvey Mudd College

Baylor University

Idaho State University

since we've been told that order is not important, that's gonna make this a combination. And we have 16 coasters that we want to choose eight of. So this is 16 times, 15 times, 14 times, 13 times nine now, because the orders are important, we need to take off the duplicate ones. So dividing by the eight factorial on the bottom, that's gonna give me on the top 518,000 from 518,918,400 and I'm gonna divide 3 40,020 which is going to give me, then the possible choices as 12,870.