Twelve people came to celebrate their ten-year reunion

Question

Twelve people came to celebrate their ten-year high school reunion. Each
person shook hands once with all the other persons. How many handshakes were
exchanged at the reunion?

Answer 1

Hi JANCY,

Suppose that the people stood on a line. Let the last person on the line be the first person to be seated, she shook hands with the other 11 and get seated, that is 11 handshakes. The second the last person shakes hands with the remaining ten and gets seated that is 11 handshakes because he shook hands with the first person to be seated, each person shakes hands with 11 people.

Add 11 handshakes for the 12 people: 11 + 11 + 11...+ 11 

Total handshakes = 11x12 =132

 

To avoid repetition of count the same handshake twice, divide the above by 2

Answer 2

With 12 people you want the all the different ways of choosing 2 out of 12 since A shakes B's hand and B shakes A's hand is the same handshake.

 

₁₂C₂ = (12x11)/(1x2) =66