Gavin Price answered question 1/26/2011 There is 7 friends (A1, A2, A3....A7).If A1 have to have shake with all without repeat. How many handshakes possible? If you mean A1 specifically, just 6. If you mean all friends without repeats, then it's 21. The logic being that the first person can shake the other 6 people's hands, then the second person can shake the other 5 friend's etc. (6+5+4+3+2+1 =21)