10 people in a party. everybody shakes hands with everybody. find the total no. of handshakes

Question

ten people are attending a party. each person shakes hands with everyone. Each person shakes hands with everyone else in the party. Find two different ways to find the total number of handshakes

Answer 1

First Way:

Since there are 10 people, and each handshake requires 2 people, this is the same as choosing 2 people out of 10 people.
Thus, the answer will be 10 C 2 = 45 handshakes

Second Way:

The first person will shake hands with 9 people, the second person will shake hands with the remainder 8, the third person with the remainder 7....
Thus, we have 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 handshakes

Answer 2

easy. 10 x 10 minus 10 is 90.

Answer 3

45 total handshakes

10*9=90

90/2=45