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great job completing the last tutorial you made both the director and the producer very happy sometimes our directors change their minds when they see their drawings translated to 3d computer graphics in fact sometimes our directors change their minds a lot and we need to be able to adapt to those changes so let's say we have a director that wants a robot with two heads but each head has to be different that is the director doesn't want a robot with two copies of the same head now a robot consists of two heads a body and arms we'd like to know how many of those we can have if we have age heads B bodies and a arms we saw that by using a tree diagram we could multiply the number of each kind of part together to get the total number of combinations well we have a choices for the first head but since the second head has to be different we only have H minus one choices for the second head as before we have B choices four bodies and a choices for arms for a total of H times H minus one times B times a combinations so it's all about multiplying together all the choices you have at each stage mathematicians make up words for everything they use the word combinatorics to refer to this type of counting the next exercise will give you a chance to practice with other combinations