Seven People at a Party: How Many Handshakes Will Occur?

How many handshakes will occur if seven people come to a party and shake hands with each other?

What is the formula to calculate the number of handshakes between 7 people at a party?

Answer:

The number of handshakes between 7 people, when each person shakes hands with every other person exactly once, can be calculated using the combination formula. In this case there will be 21 handshakes.

To calculate the number of handshakes between 7 people at a party, we can use the combination formula. This formula helps us determine the number of ways we can choose 2 people from a group of 7.

The combination formula is: nCk = n! / [(n-k)!*k!]

Where: n is the total number of options (in this case 7 people), k is the number of options chosen (2 people to shake hands), ! denotes factorial calculation.

By substituting the values into the formula, we get: 7C2 = 7! / [(7-2)!*2!] = 21 handshakes.

Therefore, there will be a total of 21 handshakes occurring when each person at the party shakes hands with every other person exactly once. It's a great way for everyone to connect and spread positivity!