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Data Analysis and Probability
Math Content:
Data Analysis and Probability

When the nine justices of the Supreme Court meet, they greet one another with a handshake to show harmony of purpose, even though their views may differ. How many handshakes occur? In general, how many handshakes occur when there are n people?

How to Use

  • Use the red points (people) to enlarge or decrease the size of the display.
  • By highlighting two or more points, the location of the display can be moved.


The buttons are meant to be used sequentially.

  • All the green buttons will show:
    • The number of handshakes between the specified number of people.
    • A diagram that shows how the handshakes are shared.
  • The gray buttons will toggle on and off to show or hide values and/or segments.
  • Use the Reset button to start over.


  • What patterns do you notice between the number of people and the number of handshakes shared?
  • If possible, what is a general formula showing the number of handshakes shared between n people? Assume that everyone shakes each other’s hand.