If 30 people are asked to have a handshake with each other. how many handshakes happen.?

435

Explanation:

Suppose there were 3 people, A, B, and C. The hand shakes would be AB, AC and BC...2+1=3

Suppose there were 4 people, A,B,C,and D. The hand shakes would be AB,AC,AD,BC,BD,CD...3+2+1=6

Suppose there were 5 people, A,B,C,D and E. The shakes would be AB,AC,AD,AE,BC,BD,BE,CD,CE,DE...4+3+2+1=10

Get the pattern?

So, you would do: 29+28+27+26+25+24+23+22+21+20+19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1

Total 435