A group of 12 people exchange handshakes. How many handshakes are exchanged if each person shakes hands exactly once with each of the other people in the room?

Question

zootedyoungin · Answer

144

zootedyoungin · Answer

24

zootedyoungin · Answer

idk

amtran_bus · Answer

U wrong

amtran_bus · Answer

Nope. Ans is 66

zootedyoungin · Answer

how is it 66

amtran_bus · Answer

I need some real help @mathstudent55 @agent0smith

mathstudent55 · Answer

Here is a circle with 12 marks on it, like the hours on a clock.
Connect each mark with all other marks and count them.
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amtran_bus · Answer

lol really? That would take awhile

mathstudent55 · Answer

12 o'clock connected to all hours = 11
Now connect 1 o'clock to all hours. Don;t connect to 12 o'clock bec that is already done.
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amtran_bus · Answer

I just need to know why it is 66. Book says (12! 2!) / 10!

mathstudent55 · Answer

That is 10 more.
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amtran_bus · Answer

ok I'm following you

mathstudent55 · Answer

You see that for each following hour you connect, you have one less connection to make.
You end up with
11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

mathstudent55 · Answer

The sequence
1 + 2 + 3 + ... + n has a sum

$\dfrac{n (n + 1)}{2} $

amtran_bus · Answer

Oh ok. I'm tempted to include the 12 but your illustration really helps a lot

amtran_bus · Answer

Thanks so much

mathstudent55 · Answer

$1 + 2 + 3 + ... + 10 + 11 = \dfrac{10(11)}{2} == 66$

mathstudent55 · Answer

Here are the numbers 1 through 11 displayed in a very specific way.
Now we will add them vertically.
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