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Intro Stats / AP Statistics
1 week, 1 day ago
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From a group of 30 people, we have to choose 14 people for a verse team and we want to find how many different ways we can choose a group of this many people. So the first thing to realize is that to solve this problem, we're going to have to use permutations and the reason for that is because, with permutations we deal with events where the order in which people are picked doesn't matter and also there can't be repetitions. So the permutations used the formula n factorial, divided by n minus r factorial, to give us the number of desired outcomes. Where n is a total amount of people we can pick from. So, in our case has 30 point, so the numerator is 30 factorial and our denominator is n, minus r, where n is 30 and r is how many people we want. So that's 14 point. So this comes out to 30 factorial divided by 30 minus 14 factorial. If we simplify this even further, this is 30 factorial divided by 30. Minus 14 is 16, so 16 factorial, and so there's gonna, be quite a large number. But i plugged this into my calculator and all my calculator says 1.267 times 10 to the nineteenth in scientific notation, and so this is our final answer and the total number of unique ways that we can choose a group of 14 from a total.
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