Question

There is a Congressman from Texas who lives in my neighborhood. He always introduces himself and shakes hands with everyone he meets-that's a politician for you! He went to a party and encouraged everyone to shake hands with everyone else. I was there and observed the following: when there were two people, they shook each others hand, so that was 1 handshake. When three people shook hands, there were three handshakes. When four people shook hands, there were six handshakes. Suppose that this was a big fundraiser for the Congressmen, and 105 people were there.
How many handshakes were there amo

Answer 1

How many handshakes were there among the 105 people?

Answer 2

lets ask him

Answer 3

let's fire him now

Answer 4

Haha funny saifoo

Answer 5

did he send pictures on his smart phone of him shaking hands too?

Answer 6

WOW GUYS. Seriously please help!

Answer 7

with a name like mathsux4real :-)

Answer 8

Cuz math sucks... for real!

Answer 9

permutation/combiantion calc

Answer 10

without math no computers, no music, no tv, no cellphone, no cars........

Answer 11

Whatever. Can you please just help me with the question?

Answer 12

aaaaah, whatever.

Answer 13

PLEASE

Answer 14

ok, first step

Answer 15

what part of math are you studying right now?

Answer 16

Algebra 2.

Answer 17

http://www.ehow.com/how_4466533_calculate-combinations-permutations.html

Answer 18

this should help you check your answers http://www.statisticshowto.com/calculators/permutation-calculator-and-combination-calculator/

Answer 19

Have you tried drawing a picture?

Answer 20

There are 105 people. 2 of them are nececery for one handshake. You can choose 2 of them on \[\left(\begin{matrix}105 \\ 2\end{matrix}\right)\] ways. It is \[52\times105\]= 5460 handshakes.

Answer 21

Thanks Gg!

Answer 22

You're welcome :)

Answer 23

Alternately, you can think of it this way:
Say there are 5 people:
The first person has 4 handshakes.
The second person has 3 handshakes (cuz he already shook hand with the first guy)
The third person has 2 handshakes (he shook hands with the first and second guy already)
The fourth person has 1 handshake.

So for five people there are 4 + 3 + 2 + 1 handshakes.

For 105 people there are 104 + 103 + 102 + ... + 3 + 2 + 1 handshakes.

:)