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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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