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the advantage of this diagram is that since it represents all of the choices we 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 2 times 3 times 3 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 multiply 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 6 bodies and 7 arms and say eight different kinds of wheels on our robots we would have to build 5 plus 6 plus 7 plus 8 or 26 different kinds of objects but we could build 5 times 6 times 7 times 8 or 1680 different robots because there are so many possible combinations it's easy to go crazy and build a huge crowd of robots 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 artistic goals 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 the 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 dollars the director and producer will be here in 10 minutes to review your work I know you got this