Question

In a party there are 20 persons If every person shook hand with every other person in the party exactly once find the total number of handshakes exchanged in the party

• A. 420
• B. 20
• C. 380
• D. 190

Answer 1

The correct option is D 190

Each person with shook hands with $19$ others.

So, $20$ persons will shook hand $=20\times 19$ times

However we crunted 1 handshakes twice.

So, total number of ways $=\frac{20\times 19}{2}=190$

Hence the answer is $190.$