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Task Assignments How many ways can an adviser choose 4 students from a class of 12 if they are all assigned the same task? How many ways can the students be chosen if they are each given a different task?

495; 11,880

Intro Stats / AP Statistics

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okay. Today's question is how many ways can advise her Choose four students from a class of 12 if they're all assigned the same task. So we are going to use combinations to answer this question because the order does not matter, um, in this question, because they're all doing the same test. So we're going to do 12 or choosing out of 12 and we're picking four of them. So we use our combination formula, which is gonna be 12 fact Toro over four fact or oh, 12 minus four factorial. So once we simplify that, we have 12 facto room over four. Fact Toro eight. Fact Toro. Now what I would do to simplify is since 12 factorial means 12 times 11 times 10 and so on an eight factory means eight times seven times six and so on. We can cancel everything out, Um, from the eight and down. So that leaves us with on the top 12 times 11 times 10 times nine. And then the rest of that cancels out on the bottom. Since I canceled out the eight fact or oh, I still have the four factorial, which is four times three times two times one. Now I multiply that I get 11 8 80 I'm a top and 24 on the bottom, which will divide to give me 4 95 So there's 495 ways of choosing those four students. The second question as Hominy can students could be chosen if they're all given a different task. So now I'm going to use permutations because the order does matter. So I'm gonna do 12 p for instead of 12. C four and the formula for permutations will be 12. Fact, Toro over 12 minus four Fact. Toro. So I get 12 fact Toro over eight fact or oh, and again, just like on the last one, that all the way up to a it's gonna cancel. So I'm just gonna have 12 times, 11 times 10 times nine, which gives me the 11,880. So there's 11,880 ways to pick those four students if they're doing different

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