Question

Mrs. Smith's class is working on a variety of science experiments. Each

student must complete one experiment with each of the other students in
the class. There are 12 students in the class. How many different groups
will be made by the end of the experiments ? Each pair of students can
only be together once.

Answer 1

66

Explanation:

If there are n students, then the number of pairs is
`(n(n-1))/(2)`.

With 12 students,
`(12(12-1))/(2) = (132)/(2)=66` pairs can be formed.

The reason the formula works is this: Each of the 12 students can be paired with 11 other students (no student is paired with him/her self). But counting 12 x 11 = 132 counts each pair twice. Example: student A can be paired with student B,..., student B can be paired with student A. The pair was counted two times.

See the attached image that shows pairings of 5 students. There are

5(5 - 1)/2 = 5(4)/2 = 10 pairs.