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Question 983010: If 8 people meet each other at a meeting by shaking hands with one another how many handshakes take place?
the answer I think is (8*7)/2 = 28 handshakes, but I don't understand it. Why is it 8*7 I know there are 8 people but why the 7? it's confusing me. Wouldn't it be a lot more. Maybe I just don't understand multiplication or something. Please explain what I don't understand about this.
Thank you
Found 3 solutions by josgarithmetic, jim_thompson5910, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Draw a picture of this, using dots arranged uniformly around a circle. Start drawing and counting ALL of the segments that are possible. NONE is to be duplicated.
A way to handle this without actually using all eight dots (representing people) is to start with just 3 dots, and draw all segments, and count. Then Use 4 dots, draw all segments and count them; 5 dots, and on like this. LOOK FOR THE PATTERN!.....ANALYZE AND LOOK FOR THE PATTERN.....
Try to find an expression (algebraic expression ) for a formula for this pattern.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! Consider a smaller example. Say there are 4 people only. Just enough to have a party, but small enough to list out all the possibilities.
I'm going to call them A,B,C,D
Draw out a 4x4 table, 4 rows and 4 columns, then place the letters along the top and left side. The inner part of the table will represent the handshake pairing.
You'll have this set of possible handshakes
AB
AC
AD
BC
BD
CD
There are 6 handshakes possible. The entire table will not be used because you can't have something like AA or BB. A person can't shake hands with him/herself. Also, something like AB is the same as BA. The order of the shake doesn't matter. That means we cross out half of the list.
The entire table is 4*4 = 16 handshakes. But we exclude AA,BB,CC,DD. So we're down to 16 - 4 = 12 handshakes. Then we exclude the ones that are double counted. If AB is listed, then we can't list BA because it's the same handshake. The pairs BA, CA, DA, CB, BD, DC are kicked out as well because they are already listed above. The 12 drops to 6 (since 12-6 = 6)
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Alternative method:
Think of 2 slots: X and Y
For slot X we have 4 choices to fill it. For slot Y, we have 3 choices. We don't have 4 choices because we cannot pick anyone twice. Multiplying these out we get 4*3 = 12. We divide by 2 to avoid double counting. AB is the same as BA. So 12/2 = 6 giving us the same answer.
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All of that above is for the example. In your particular problem, the answer is indeed (8*7)/2 = 28 because there are 8 people for the first slot. Then 7 for the next slot. Making 8*7 = 56 permutations. Since order does NOT matter we divide by 2 to avoid double counting.
Hopefully this is making sense. If not, then please let me know.
Answer by MathTherapy(10555)  (Show Source):
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