Question

In a party every person shakes hands with every other person. If there was a total 30 persons in the party, find the number of shake hands that happened

Answer 1

The 30th person shakes hand with all person present except him .
handshakes=29.
the 29th person had already shakes hands with the 30th person so he hand shakes with 28 more .
Now handshakes=29+28
The 28th person had already shaked hand with 29th and 30th person.
So now handshakes =29+28+27
Now if we continue this calculation till the first person we get that :
handshakes=29+28+27+26.......+2+1
=29×30/2=29×15=435

Hope this helps :)

Answer 2

Total number of people =30

First man will do handshakes with 29 people.

Second person will do with 28 people because he has already done with one person.

Hence the no.of handshakes will be of form:-

29+28+......1

This an AP

1+2+3...29

Sum of AP=n/2*(a+(n-1)d)

=29/2*(1+29*1)

=29/2*30

=29*15

=435

Thanks.