Question

[PROBABILITY] THERE ARE FOUR PEOPLE IN A ROOM THAT HAVEN'T MET BEFORE. THEY ARE TOLD TO SHAKE HANDS, EXACTLY ONCE, OF EVERY OTHER PERSON IN THE ROOM SO THAT THEY ALL MEET EACH OTHER. IF EACH OF THESE PEOPLE SHAKE THEIR HANDS WITH EVERY OTHER PERSON EXACTLY ONCE THEN HOW MANY HANDSHAKES ARE GOING TO OCCUR?

Answer 1

6

Explanation:

Let the 4 people be A, B, C and D. If each of them shakes hands with another person exactly one time then that means

A shakes with B, C and D. So 3 handshakes

B already shakes with A. So B shakes with C and D. 2 handshakes

C already shakes with A and B. So C shakes with D only. 1 handshake.

D already shake hand with all above.

Total handshakes: 3 + 2 + 1 = 6