Explanation

In this question, let's imagine these 8 people lined up in a row, and imagine how we can pair them up. We can call the people A through H. There are seven ways to pair up person A with another person. That's true for each of the 8 people, so we have . But we have counted all the pairs twice. For example, 7 ways to find a pair for A counted AB, and 7 ways to find a pair for B counted BA. Therefore, we must divide by 2. The number of pairs is therefore 28. The correct answer is (C).

Another way to reach the answer starts the same: there are seven ways to choose a partner for A. Then, excluding the pair already counted, there are 6 ways to find a partner B that haven't been counted yet. There are 5 for C, and so on. So we have 7+6+5+4+3+2+1 =28 possibilities. This technique can be used for larger numbers also, because you can use the average formula to determine the sum of the numbers.

Again, the correct answer is (C).