a) If there are 16 people, the 1st person could be friends with 15 other people. The 2nd person can also be friends with 15 other people, however, one of those people we already counted, so we need to exclude that person in order to not DOUBLE COUNT. So the 2nd person can be friends with 14 other people.
Continuing the pattern, the 3rd person can be friends with 13 other people, 4th person with 12 other people, etc...
So the answer is: 15 + 14 + 13 + 12 + ... + 2 + 1 = 120 pairs (line segments)
b) At the end, there were two groups. One group had 10 people who were all friends with each other, but not friends with the other group of 6 people. And the other group of 6 people were all friends with each other, but not friends with the other group of 10 people.
So the group of 10 people had: 9 + 8 + 7 + ... + 2 + 1 = 45 pairs
And the group of 6 people had: 5 + 4 + 3 + 2 + 1 = 15 pairs
For a grand total of 60 pairs (line segments)
