There are ten people in the room and everyone shakes hands with everyone else, how many handshakes occurred?
Question
There are ten people in the room and everyone shakes hands with everyone else, how many handshakes occurred?
Solution
To solve this problem, we can use the formula for combinations in mathematics. The formula is:
nCk = n! / [(n-k)! * k!]
where:
- n is the total number of items,
- k is the number of items to choose,
- "!" denotes a factorial, which means multiplying all positive integers up to that number.
In this case, we have 10 people and a handshake involves 2 people. So, n=10 and k=2.
Substituting these values into the formula, we get:
10C2 = 10! / [(10-2)! * 2!] = 109 / (21) = 45
So, there are 45 handshakes.
Similar Questions
At the end of a banquet 10 people shake hands with each other. How many handshakes will there be intotal?
There are 20 people in a party. If every person shakes hand with every other person, what is the total number of handshakes?
12 people at a party shake hands once with everyone in the room. How many handshakes took place?Choices:- 77 54 78 66
8 men entered a lounge simultaneously. If each person shook hands with the other, then find the total no. of hand shakes ?
Five men, Kevin, Roly, Brian, Max and Brice were at a party. Each of the men shook hands with each of the other men. How many handshakes were there?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.