WEBVTT
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Marilyn invited four of her 24 friends over for a movie night.
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If she chose to invite her friends at random, what is the probability that Cynthia, Ashley, Angelina, and Sandra are chosen?
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The number of ways we can choose four friends from 24 friends is by 24 choose four.
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The formula for combination is π choose π, where π in this case will be 24 friends and weβre choosing four of them, that would be π, which is equal to π factorial divided by π factorial times π minus π factorial, which means we have 24 factorial divided by four factorial times 24 minus four factorial.
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So we have 24 factorial divided by four factorial times 20 factorial.
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Twenty-four factorial is 24 times 23 times 22 times 21 all the way down to one.
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And then four factorial is four times three times two times one.
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And 20 factorial is 20 times 19 times 18 times 17 all the way down to one.
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Here we can see the twenties, the nineteens, the eighteens, the seventeens, all the way down to ones can cancel.
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So we have 24 times 23 times 22 times 21, which is 255024 all over four times three times two times one, which is 24.
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And now we divide these numbers and we get 10626.
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So the probability of these girls being chosen, where the order doesnβt matter, would be one out of 10626.