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there are 10 students in Mr. Alvarez's art class. Throughout the year, each student must pair up with every other student to complete a project. How many projects will be completed?
45?

combinations of ten taken two at a time:

10!/[(2!)(8!)] = 10*9/2 = 5*9 = 45

I am trying to think how I would have done this in grade 7. I assume you have not had permutations, combinations and factorials.
make a table of combinations
first person shakes hands with 9 --> 9 projects
second with 8 --> 8 more
third with 7 --> 7 more
etc
9+8+7+6+5+4+3+2+1 = 45

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