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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1200.0. "Connecticut 6/44 lotto problem" by VMSDEV::HALLYB (The Smart Money was on Goliath) Sun Mar 04 1990 00:24

    I see we haven't had a lottery problem in a long time.
    
    In the Connecticut lottery 6 numbers are drawn from 1-44.
    
    Lottery sales agents can sell you "quick-picks", where the machine
    generates random valid tickets and lists the numbers in ascending order.
    
    Tickets can hold up to 5 such picks.
    
    On a recent trip to CT my wife bought $20 worth of quick-picks,
    4 tickets with 5 random entries per ticket.
    
    Back in the car she noticed that each ticket had one or more entries
    with the same first (lowest) number.  She was surprised by this.
    Should she have been?
    
    This can be solved by brute force.  Can it be estimated via shortcut?
    
    There was also a case where two different quick-picks started with
    the same 3 first (lowest) numbers.  What were the odds of this event?
    
      John
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