Eight people are at a party. Everyone shakes hands once with everyone else. How many handshakes are there altogether?

Answer 1

To calculate the number of handshakes, we can use the combination formula.

Since each person shakes hands with every other person, each person will shake hands with 7 other people (since they don't shake hands with themselves).

So, for each person, there are 7 potential handshakes. However, this counts each handshake twice (once for each person involved in the handshake).

Therefore, we need to divide the total number by 2 to avoid counting each handshake twice.

Using the combination formula:
C(n, k) = n! / (k! * (n - k)!)

where n = 8 (the number of people) and k = 2 (the number of people involved in each handshake)

We can calculate the number of handshakes:

C(8, 2) = 8! / (2! * (8 - 2)!)
= 8! / (2! * 6!)
= (8 * 7 * 6!)/(2! * 6!)
= (8 * 7) / (2 * 1)
= 28

So, there are 28 handshakes altogether at the party.