Five people are in a room for a meeting. When the meeting ends, each person shakes hands with each of the other people in the room exactly once. The total number of handshakes that occurs is
(A) 5
(B) 10
(C) 12
(D) 15
(E) 25
Five people are in a room for a meeting. When the meeting ends, each person shakes hands with each of the other people in the room exactly once. The total number of handshakes that occurs is
(A) 5
(B) 10
(C) 12
(D) 15
(E) 25

## Solution

Each of the five people in the room will shake four others' hands. This gives us 20 handshakes, except each handshake is counted twice (Person X shakes Person Y's hand and Person Y shakes Person X's hand), so we have to divide the total by 2 , to obtain 10 handshakes in total.

ANswer: (B)