Answer:for n people the total hand shake will be (n*(n-1))/2
Step-by-step explanation:1. The first person shakes hands with the other (n-1) people.
2. The second person shakes hands with the remaining (n-2) people (excluding the first person).
3. The third person shakes hands with the remaining (n-3) people.
4. This pattern continues until the last person shakes hands with the remaining one person.
To calculate the total number of handshakes, we can sum up the number of handshakes in each step.
Since each person shakes hands with (n-1) other people, we can express it as follows:
(n-1) + (n-2) + (n-3) + ... + 1
The sum of the numbers from 1 to (n-1) can be calculated using the formula for the sum of an arithmetic series:
Sum = (n-1) * (n-1 + 1) / 2
Simplifying further, we get:
Sum = (n-1) * n / 2
So, if n people shake hands with one another exactly once, the number of handshakes would be (n * (n-1)) / 2.