[Solved] At the end of a meeting all the ten people present shake han (2024)

Given:

Number of people in the conference = 10

Each person shakes hands with others.

Concept used:

When n people shake hands with each other, the total number of handshakes =nC2

Calculation:

Total number of handshakes =10C2= (10× 9)/2 = 45 handshakes.

When 10 people are shaking hands, each one will shake hands with 9 others.

Then the total number of handshakes = 10× 9 = 90

(Remember that, when A shakes hands with B, B is also shaking hands with A. That means, we are counting one handshake twice, one from A's side and the other from B's side)

The total number of handshakes in actual = 90/2 = 45 handshakes.

∴ The total number of handshakes is 45.