ms. beckman invites 5 of her friends to her birthday party

Question

how many handshakes are there if each person at the party shakes hands with every other person at the party?

Answer 1

Here are two ways to do this problem. Let's use 6 people (Ms. Beckman plus 5 friends, if you use 5 your answer would end up being 10 handshakes).

 

Method 1:

Let's model this by assigning each person a letter:

a b c d e f <-- our 6 people

 

The handshakes would be:

 

ab
ac
ad
ae

af

bc
bd
be

bf

cd
ce

cf

de

df

 

ef

 

Which would be 5 + 4 + 3 + 2 + 1 = 15 handshakes

 

 

Method 2:

Another way to do this problem is by using a combination formula:

n! / (r! (n-2)!)

 

where n = 6 (number of people),

and r = 2 (the number of people involved in each handshake)

 

(6!)/(2! x 4!)

(6 x 5 x 4 x 3 x 2 x 1)/((2 x 1) x (4 x 3 x 2 x 1))

720/48

15 handshakes

 

You get 15 handshakes with either method.

Hope this helps!

 

Answer 2

Hi Jennifer;

The first person will shake hands with four other people.

The second person already shook hands with the first.  Therefore, this person will shake hands with three other people.

The third person already shook hands with the first and second.  Therefore, this person will shake hands with two other people.

The fourth person already shook hands with the first and second and third.  Therefore, this person will shake hands with one other person.

The fifth person shook hands with everyone else.

 

4+3+2+1=10 handshakes