The answer is 32

For the first person, you have eight different choices. For the second person, you have seven people remaining, but one cannot be chosen because he or she is in a pair with the person chosen the first time, so you have six choices. For the third person, you have six people remaining, but two cannot be chosen because they are in pairs with those who had been chosen, so you have four choices. 8x6x4 gives you the permutation, but in this case order doesn't matter, so divide by 6 (the number of ways to arrange three objects in a row) to get the combination, which is 32.