Question

At the end of a business conference, the ten people present all shake hands with each other once. How many handshakes will there be altogether?

• A. 20
• B. 45
• C. 55
• D. 90
• E.

Hint:

In handshake problems, use the combination formula to determine the total number of possible handshakes.

Answer 1

The Correct Option is B

For each handshake, two people shake hands. The total number of handshakes can be found using the formula for combinations \( C(n, 2) \), where \( n \) is the number of people: \[ C(10, 2) = \frac{10 \times 9}{2} = 45. \] Thus, the total number of handshakes is 45. So, the correct answer is (b) 45.