akhilsuhag wrote:There are 10 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?
A) 15
B) 30
C) 45
D) 60
E) 120
The total number of pairs that can be formed from 10 people = 10C2 = 45.
If all of these pairs shake hands, each person in the room will shake hands with EVERY OTHER PERSON in the room.
The result will be 9 HANDSHAKES PER PERSON.
Since we want only 3 HANDSHAKES PER PERSON, we must divide by 3:
45/3 = 15.
The correct answer is
A.
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