Question

In a circular hall with 10 people, each person shakes hands. How many handshakes occur?

A) 45
B) 55
C) 90
D) 100

Answer 1

In a circular hall with 10 people where each person shakes hands with one another, the number of handshakes is a) 45. This is computed using the formula for handshakes in a group, which is ½ * n * (n - 1) where n is the number of people.

Step-by-step explanation:

To solve the problem of how many handshakes occur in a circular hall with 10 people where each person shakes hands with each other, you can use the formula for the number of handshakes in a group: ½ * n * (n - 1), where n is the number of people. Here, n=10. So the calculation would be ½ * 10 * (10 - 1) which equals ½ * 10 * 9 = 45. Therefore, 45 handshakes occur. Option A) 45 is the correct answer. This is a standard problem in combinatorics, a branch of mathematics dealing with counts and arrangements of objects.