how many handshakes?

Question

there are 8 people at a partyif they all shake hands, how many handshakes will there be? and can i make an equation that could find the amount?

Answer 1

1st person shakes with 7, next with 6 more etc
total is 7+6+5+4+3+2+1=7*8/2=28 handshakes.
for n people there will be n(n-1)/2 handshakes.

Answer 2

It's easiest to think about this as if the partygoers are in a line. The first person will shake hands with seven other people. The second person has already shook hands with the first, so he/she will need to make six more handshakes. The third will shake hands five more times, etc.

In general, the formula is
(n-1)+(n-2)+(n-3)+...+(n-(n-1))+(n-n)
which simplifies to
(n)(n-1)/2

Answer 3

28 handshakes n(n-1)/2 n=total numbers of people

Answer 4

yup gave you the correct answer and a general formula that will work.

I wanted to add that this is the same question as how many lines you would draw between n points. There are more general ways of expressing this but you probably get the picture for a two dimensional space. What would be the formula for an n-dimensional space?

Answer 5

56 hankshakes because 1 person can handshake 7 people (since he/she cant hankshake themselves) so 7times 8= 56

Answer 6

for first person ........7
for second ..............6
third ...................5
and so on

your will get
7+6+5+4+3+2+1+0=28


is that from a math contest?
when i was doing it for the first time, i drew a circle and placed 8 dots on the circle and connected each one to the other ones, then counted the lines by highlighting them

Answer 7

answer = 8!

type that in a calculator