Posted by **rawr... im a dinosaur.... rawr** on Thursday, October 18, 2012 at 3:36am.

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?

- Algebra Grade 7 -
**Damon**, Thursday, October 18, 2012 at 5:01am
combinations of ten taken two at a time:

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

- Algebra Grade 7 -
**Damon**, Thursday, October 18, 2012 at 5:02am
Grade 7 ????

- Algebra Grade 7 -
**Damon**, Thursday, October 18, 2012 at 5:06am
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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