Question

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

Answer 1

Answer:

66

Step-by-step explanation:

If there are  n  students, then the number of pairs is $\frac{n(n-1)}{2}$.

With 12 students, $\frac{12(12-1)}{2} = \frac{132}{2}=66$ 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.