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?

This problem can be solved using the formula for combinations. In this case, we are looking for the number of ways to choose 2 people (to shake hands) from a group of 5. The formula for combinations is:

C(n, k) = n! / [k!(n-k)!]

where:

• n is the total number of items,
• k is the number of items to choose,
• "!" denotes factorial, which is the product of all positive integers up to that number.

So, in this case, n = 5 (the number of men) and k = 2 (since a handshake involves 2 people).

Substituting these values into the formula gives:

C(5, 2) = 5! / [2!(5-2)!] = (54321) / [(21)(321)] = 120 / [2*6] = 120 / 12 = 10

So, there were 10 handshakes at the party.