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CAHSEE practice: Problems 15-16

Video transcript
Problem 15. A restaurant is advertising 3-item combination specials that must include a main dish, a vegetable, and a drink. OK, so you have to have at least one of these. So what are they going to ask us? How many 3-item combinations include a soft drink and a corn? So let's reread what the conditions are. A restaurant is advertising 3-item combination specials that must include a main dish, a vegetable, and a drink. So you pick one from each of these buckets. So they're already picking two of the buckets for us. It includes a soft drink, and it has to include a corn. So they've essentially already picked our choices from this bucket and that bucket right there. And they're saying, how many combinations are left? Well, we only have two choices. We only have freedom when it comes to picking the main dish. Because the problem has already picked for us our vegetable and our drink, the corn and the soft drink. And so there's only two possible main dishes, so those are the 3-item combinations that include a soft drink and a corn. There's two possible ones, chicken and beef. So it's two. Just to make sure you understand that, what are the two combinations, just to make it explicit? Well, one combination is chicken, corn, and soft drink. Right? They're forcing the corn and the soft drink on us. And then the other combination is beef, corn, and soft drink. That's the second combination, because they're forcing the corn and the soft drink on us. So there's two combinations. But the way I just thought about that is this thing has been constrained for us, the vegetable and the drink, so you can ignore it. And so how many combinations of main dishes are there? Well, there's two. I just counted them. Chicken and beef. Problem 16. Donald priced six personal Compact Disc players. And they wrote the CD right there. The prices are shown below. OK, so these are six CD players. What is the median price? So the trick of this problem is just knowing what median means. Median literally means the middle price. So if I were to put all of these numbers in order, which I'm going to do right now, the median is going to be the middle number. So let's put them in order. What's the smallest number here? 21. Cross that out. And then we have another 21. So let me write that down. I'll cross that out, make sure I know I used it. The next largest number is 23. So let me cross that out. The next largest number is 25. Cross that out. Next largest number is 31. Cross that out. And then the next number is 39. So what is the middle number here? Well, you see we have six numbers, and, actually, there is no middle number. If we have an even number of numbers, there's no single middle number. There's two numbers that we can kind of view as the middle. These two numbers here are the middle. Right? I can't say 23 by itself is the middle, because there's two above it and three below it. And I can't say 25 is the middle, because there's two below it and three above it. So when you have an even number of, I guess, data, like you have right here, you pick the middle two. If I had the numbers 1, 2, and 3, then I could just pick the 2. But if I have 1, 2, 3, and 4, I have to pick the middle two numbers. So here I pick the middle two numbers, and I need a median. And so what I do is I average these middle two numbers. I take the mean, or I go right in between them. So what's exactly in between 23 and 25? Well, you can do that in your head. It's going to be 24. But if you can't do it in your head, you literally would just add those two numbers, 23 plus 25, and then divide by 2. So this is going to be equal to 48 divided by 2, which is $24. And I just explained that to you, and just in case you got the situation where these are some weird decimal numbers, or these were much larger numbers, where you couldn't just say, hey, 24 is right in between those two guys right there.