How many unique handshakes if each person in a group of 10 give handshakes out to each and every other individual. (a) 100 (b) 50 (c) 45 (d) 20 (e) 10

true, or 9+8+7+...+2+1

None of those answers are correct. The follow-up question should be are we assuming that each person is only using 1 hand? For example, if everyone is only giving handshakes left to left, or left to right or right to right or right to left? Granted left to right and right to left would be awkward.

45. Imagine it as a polygon of side 10. Or draw out triangle, square, pentagon, and see the pattern yourself, if you don't know the algorithm.

I don't know why the person above doesn't say that n(n-1)/2 where n is the number of people in the group the intuition is that every person in the group (n) has to shake every other persons hand (n-1) and then we only want to count each interaction once.

Or just do: (10 Combination 2) = 10!/(2!8!) = 45