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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.