During the African-US summit last year, 10 presidents left the conference room and greeted one another. Assuming no 2 presidents repeatedly greeted themselves, **how many total handshakes were effected?**

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Answer is 45 handshakes. The first president greeted 9 presidents, the second 8 and so on, so 9+8+7+6+5+4+3+2+1. This gives 45 handshakes.

in permutations and combinations way

A handshake is possible with two people, so it is similar to How many ways you can select two people out of 10.

i.e. 10C2 = 10!/(8!*2!) = 9*10/2 = 45