Question

At a party, each person shakes hands once with every other person at the party. How many handshakes will happen if there are: a) 4 people at the party? b) 5 people at the party? c) 11 people at the party?

Answer 1

a) Six handshakes

b) Ten handshakes

c) 55 handshakes

Explanation:

With every "set" of handshakes by a person, it decreases by one. Im pretty sure you cant handshake with yourself xD, so that's why it decreases by one every time. For example with 4 people at the party, the first person shakes the other people's hands, which is three, and which is also 4-1 which equals 3. Then with the second person in line at the same party, shakes the other people's hands, but not the first person in line cause they already had a handshake, which is two, and which is also 3-1 which equals 2. And u know how it goes. Until it gets to the last person in line, they can't have a handshake with themself so the number ends. Then you add all those numbers together and you have the answer.

If u dont really understand what i just said then you can draw the diagram yourself and you'll see

Answer 2

there will be 55 handshakes.

Explanation:

If there are n people at a party and each person shakes hands once with every other person, we can count the number of handshakes by adding up the number of handshakes each person has.

For example, the first person shakes hands with n-1 other people, the second person shakes hands with n-2 other people (since they already shook hands with the first person), and so on. The last person does not need to shake hands with themselves, so they shake hands with n-1 other people.

Therefore, the total number of handshakes is given by the formula:

(n-1) + (n-2) + ... + 2 + 1 = (n*(n-1))/2

a) If there are 4 people at the party, the total number of handshakes is:

(4*(4-1))/2 = 6

So there will be 6 handshakes.

b) If there are 5 people at the party, the total number of handshakes is:

(5*(5-1))/2 = 10

So there will be 10 handshakes.

c) If there are 11 people at the party, the total number of handshakes is:

(11*(11-1))/2 = 55

So there will be 55 handshakes.