## anonymous one year ago In a meeting of 14 people, if they will all shake each other hands this number will be how many?

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1. anonymous

This is a combination problem

2. anonymous

every individual gets to shake hands and "interact" with 13 others

3. anonymous

Also please specify the number of possible ways in which handshake can be done or number of handshakes this wording is f:ed up

4. anonymous

Your wording seems to imply just multiply by 2 the number of hands or handshakes

5. anonymous

For the first person, handshakes=13(you can't shake hands with yourself, well technically you can but we won't count that here) For the second person, as he has already shaked hands with first person, he needs to shake hands with 13-1=12 people you can keep going on on with this and basically this amounts to $13!=13\times12\times11\dots1$

6. mathmate

hint: Remember 2 things for the "handshake problem" for a group of n people 1. Everyone shakes hands with (n-1) othes, so there are n(n-1) "shakes". 2. Since we have counted the handshakes from both ends of the shake, we have double counted, so the above number must be divided by two to get the true number of hand shakes. Take the example for 6 people below: |dw:1439293778988:dw| The above diagram shows a complete graph of order 6, equivalent to 6 people. Each side/diagonal represents a handshake between the people from A to F. The number of lines is the number of handshakes we're after.

7. mathmate

For six people, the number of handshakes is n(n-1)/2 = 6*5/2=15.