Question

There are 10 people in a room. If everyone shakes everyone else's hand exactly once, how many handshakes occurred?

Answer 1

Have you studied combinatorics?

Answer 2

3+2+1=6 etc...

Answer 3

@calculusfunctions No I haven't

Answer 4

No guys. those are the wrong answers. You're not helping him/her.

Answer 5

@calculusfunctions Her... So that you've been assured

Answer 6

@Kainui what is the equation you are using?

Answer 7

10! =3628800

Answer 8

There's a story that when Gauss was a kid he had to add up all the numbers from 1 to 100 so instead of doing that he just realized:

1+100 is the same as 2+99 which is counting up and down all the way to 50+51. So you can add up the first and last...

Equation? Just interpret the pictures. It speaks for itself.

Answer 9

Lol @Luis_Rivera

Answer 10

@Luis_Rivera Huh?

Answer 11

think of n people as n noncollinear points where every point is connected to every other point. Then there are\[\frac{ n(n -1) }{ 2 }\]line segments. Now @ontour you try it.

Answer 12

Yeah think of them like n noncollinear points. That's accessible language to someone learning math, not full of jargon and unnecessarily unhelpful.

Answer 13

Answer's 45 dudes...

Answer 14

Yes! perfect!

Answer 15

9+8+7+6+5+4+3+2+1=45

Answer 16

Excellent @ontour !

Answer 17

Go back and look at the pictures I drew, I promise that will make your life a million times easier if you imagine 3 people shaking hands or 4 people, then you can figure it out for yourself to know it's true.

Answer 18

THANK YOU GUYS HAHA @calculusfunctions @Kainui @S0fw0N

Answer 19

@Kainui I didn't really understand your pictures I understand what you wrote... I',m going to try to understand them though

Answer 20

the letters represent people, the lines represent handshakes. So "a" shakes hands with b and c. Then b and c shake hands. No more hands to shake.

Just realize that after someone's shaken hands with everyone else then they can be removed. It starts at one less than the total number of people because you can't shake hands with yourself. I mean, you could, but, uh...

Answer 21

Hahahahaha @Kainui I got your point. I mean, the more simplified way of saying that would be 8(7)=56 but then divide that by 2

Answer 22

{_ {10}}P_{10} = \frac{10!}{(10-10)!} = 3628800

Answer 23

@Luis_Rivera F U N N Y

Answer 24

Huh, 8*7? What?

Answer 25

Given 8 people, each person shakes the hands of 7 other people.

Answer 26

:)

Answer 27

@Luis_Rivera You just made my day using math. Never thought I would say that or that it was even POSSIBLE

Answer 28

Nope, not so ontour. 8 people in a room is 36 handshakes!

Answer 29

no seriously

Answer 30

So think about the 8 people in the room. One guy shakes everyone else's hands which means 7 handshakes happen. He leaves and now there are 7 people in the room. Another guy does the same thing, but since there's one less person he can only give 6 handshakes.

This happens until everyone is gone:
7+6+5+4+3+2+1

Answer 31

There are n people and only two can shake hands. Thus there are n "choose" 2 ways of accomplishing this task. If you haven't learned combinatiorics, that's fine. If there is a "nCr" button on your calculator, you can use that.