Out of 123 persons, the first person will shake hand with 122 persons.
The second person will shake hand with 121 persons (because he has already shaken hand with first person).
The third person will shake hand with 120 persons and so on. The second last person shakes hand with only one person. And last will shake hand with none
(because he has already shaken hand with all persons).
In order to find the total number of handshakes you have to add all the natural numbers from 1 to 122 i.e. ∑ 122.
∑122 = 123 x 122/2 = = 7503 handshakes.