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Question

There are 6 people in a room. If everybody shakes hands once with each person, how many handshakes will there be?

Answer 1

combinations class 2 of 6 elements is

C(6,2) = 6 * 5 / 2 = 15

Answer 2

15. Imagine that the 6 people were lined up in the room. The first person goes down the line and shakes the hands of the 5 other people. Having shaken everyone else's hands, he leaves the room. The second person now goes down the line and shakes the hands of the other 4 people and leaves. This continues, so the third person shakes three hands, the fourth two, and the fifth one. The sixth person is left alone, because everyone else shook her hand before they left, so she can leave as well. 5+4+3+2+1=15.

Answer 3

oh shakes hands only once then its 15 b\c 6 people, 1 person shakes 5 peoples hands. 2nd person shakes 4. 3rd person shakes 3. 4th person shakes 2. 5th person shakes 1, 6th person shakes none b\c hes only one left and he cannot shake his own hand. so = 15 because they cannont repeat shaking the other persons hand since they already shaked it their turn which is why the number decreases every time.