Question

There are 18 students in Mr.Alvarez’sart class. Throughout the year, every student must pair up this every other students to complete a project. How many projects will be finished? (A) 135 projects (b) 149 projects (c) 153 projects (d) 171 projects

Answer 1

This is the same as the shake-hand problem.
Consider when two students pair-up to do a project, they are shaking hands, i.e. the handshakes do not get counted twice, one from each student.

So with 18 students, each students gets to pair up with 17 other students to make 18*17=306 projects.

However, since we don't count each project twice, we end up with 306/2=153 projects.