Posted by **donna** on Thursday, April 22, 2010 at 10:56pm.

At a party, there were 105 handshakes. If each person shook hands exactly once with every other person, how many people were at the party?

- math -
**Reiny**, Thursday, April 22, 2010 at 11:00pm
for n people there will be C(n,2) handshakes

C(n,2) = 105

n!/(2!(n-2)!) = 105

n(n-1)/2 = 105

n^2 - n - 210 = 0

(n-15(n+14) = 0

n = 15 or n=-14, but n > 0

so there were 15 people

- math -
**sakshi**, Saturday, April 16, 2016 at 1:20pm
Good

## Answer This Question

## Related Questions

- math - How many people were at a party if There were 105 handshakes at a party ...
- 7th grade - At a party, there were 105 handshakes. If each person shook hands ...
- math - taylor was having a party.she invited 20 friends to her party, if each ...
- math - At a party everyone shook hands with everyone exactly once there were a ...
- Math1 - An undisclosed number of friends gather for dinner. Each person shakes ...
- math - At the medal presentation, each person shook hands with every other ...
- Math(Please Help!) - An undisclosed number of friends gather for dinner. Each ...
- Algebra - A scientist wants to research the potential spread of germs by contact...
- maths - Please help. Thank you Fourteen people attend a meeting. If each person ...
- Math - At a party, 55 handshakes took place as everyone shook hands with ...

More Related Questions