Posted by **mark** on Sunday, February 10, 2013 at 8:06pm.

taylor was having a party.she invited 20 friends to her party, if each person shook hands with every other person .how many handshakes would there be? please explain,thanks

- math -
**Ms. Sue**, Sunday, February 10, 2013 at 8:09pm
21 * 20 = ?

- math -
**Reiny**, Sunday, February 10, 2013 at 9:38pm
Each of the 20 people will shake hands with 19 other people

20(19)= 380

but that would include duplicates such as A shaking hands with P, and P shaking hands with A, which is the same handshake

so number of handshakes = 20(19)/2 = 380/2 = 190

or

we are choosing pairs from 20

= C(20,2) = 190

- math -
**Ms. Sue**, Sunday, February 10, 2013 at 9:40pm
Thanks, Reiny -- I goofed and didn't consider that we can't count A and P and P and A.

I included the hostess -- so we have 21 people.

- math -
**Reiny**, Sunday, February 10, 2013 at 10:11pm
Thanks Ms Sue, and I didn't catch the hostess part, only saw the 20.

So let's go with your answer ÷ 2 = 21(20)/2 = 210

## Answer this Question

## Related Questions

- math - How many people were at a party if There were 105 handshakes at a party ...
- math - At a party, there were 105 handshakes. If each person shook hands exactly...
- 7th grade - At a party, there were 105 handshakes. If each person shook hands ...
- maths - Please help. Thank you Fourteen people attend a meeting. If each person ...
- Algebra - A scientist wants to research the potential spread of germs by contact...
- math - At a party everyone shook hands with everyone exactly once there were a ...
- Math - At a party, 55 handshakes took place as everyone shook hands with ...
- Math - At a party, 55 handshakes took place as everyone shook hands with ...
- Math - Sr. John and his wife went to a party where four other married couples ...
- math - If 8 people went to a party and each person shook hands at least one time...

More Related Questions