Fourteen family members have a one on one video chat with eachother to wish eachother a happy new year. How many video chats occurred?

Question

Fourteen family members have a one on one video chat with eachother to wish eachother a happy new year how many Video chats occurred 

Answer 1

Let's call the family members X1, X2, X3, ..., X14.

Start with X1: (s)he has a video chat with X2, X3, ..., X14, for a total of 13 "new" video chats.

Now for X2: (s)he has a video chat with X1, X3, X4, ..., X14, but we already counted his/her video chat with X1, so there are 12 "new" video chats.

X3: unique video chats with X4, ..., X14, for 11 "new" video chats

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X13: unique video chat with X14, for 1 "new" video chat.

X14: no "new" video chats (that haven't previously been counted)

So 13 + 12 + 11 + ... + 1 = 13(14) / 2 = 182 / 2 = 91 video chats.