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- The advantage of this diagram, is that since it represents all of the choices you have, we can just add more and more choices to the bottom. So, if we have two heads and three bodies and three arms, then the diagram would look like this, for a total of two times three times three, or 18 different combinations. These are sometimes called tree diagrams, because when you turn them over, they look a lot like a tree. The diagram has helped us understand that we just need to multiple the number of each kind of part. So, if we're just interested in how many combinations are needed, we don't need the diagram anymore. And, the number of combinations gets big fast. For instance, if we had five heads, six bodies, and seven arms, and say, eight different kinds of wheels on our robots, we would have to build five plus six plus seven plus eight, or 26 different kinds of objects. But, we could build five times six times seven times eight, or 1,680 different robots. Because there are so many possible combinations, it's easy to go crazy and build a huge crowd of robots. (robots flying through the air and rolling across the floor) (crashing and squeaking) - Emmet! - While a big crowd of robots might make the film more exciting, we have to keep in mind that the more robots there are, the more robots the animators have to animate and the more robots the computer needs to deal with. So, we're always trying to achieve our artisticals in the most efficient way possible. Now, it's time to put you to work. Your job with this interactive, is to make both the director and the producer happy. You should have a wide variety of robots, so that there's a lot of visual interest and the director is happy with your work. But, you should keep the cost down, so that the producer is happy with your work. The cost of each part is shown, select a subset of heads, bodies, and arms so that combining them in all possible ways gives exactly 12 robots and the cost of all the parts must be below $300. The director and producer will be here in 10 minutes to review your work. I know you got this.