Question

Eight people were at a party. If each person shook hands with every other person, how many handshakes were there?

a) 20
b) 28
c) 36
d) 56

Answer 1

Using combinatorics, we find that the total number of handshakes at a party with 8 people, where each person shakes hands with every other person, is 28 handshakes (option b).

Step-by-step explanation:

The question asks for the number of handshakes that occur when each person at a party shakes hands with every other person. To solve this, we can use a simple formula from combinatorics, which is a branch of mathematics. The formula to find the number of handshakes (H) for n people is H = n * (n - 1) / 2.

In this case, there are 8 people at the party, so we plug 8 into our formula as the value of n.

H = 8 * (8 - 1) / 2
H = 8 * 7 / 2
H = 56 / 2
H = 28

Therefore, there were 28 handshakes at the party, which corresponds to option b).