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Math Help - Handshake problem

  1. #1
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    Handshake problem

    I would appreciate some help with this problem.

    This is all the information I have --

    10 People in a room. Each person shakes hands with 5 people. How many handshakes take place?

    I want to say 50 -- but that would seem too easy.

    Thank you in advance for your help.
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  2. #2
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    Quote Originally Posted by SoConfused14 View Post
    I would appreciate some help with this problem.

    This is all the information I have --

    10 People in a room. Each person shakes hands with 5 people. How many handshakes take place?

    I want to say 50 -- but that would seem too easy.

    Thank you in advance for your help.
    Round 1

    Put 5 people standing in a line
    The other 5 people shake hands with them, that's 5 handshakes.

    Round 2

    Let the 5 people in the line stay where they are and move the other 5 onto the next person, with the original first of them moving around to the end.
    That's another 5 handshakes.

    Continue to rotate the 2nd group to get 5+5+5 more handshakes.

    In this way each person shakes hands with 5 other people.
    However, that's not the only way.

    In total, there are 5(5)=25 unique handshakes.
    However, there are alternative versions of these 25 handshakes.
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