another counting principle question?

Question

There are 50 people in a room, how many handshakes are there if any tow person an only shake hands once?

Answer 1

Each of the 50 people would shake hands with each of the remaining 49 other people. However, each handshake would be counted twice, by each of the two people involved, so we must divide this product by 2 to get the correct number of handshakes. The total is therefore 50 * 49 / 2, or 1225.

Answer 2

50 + √50= answer

Answer 3

n = 50(50 + 1)/2 = 1,275