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Calculating Odds

Topic closed. 2 replies. Last post 8 years ago by rayal.

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jimjwright's avatar - Yellow 3.png
Park City, UT
United States
Member #69864
January 18, 2009
993 Posts
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Posted: February 7, 2009, 4:14 pm - IP Logged

Hello,

I recently donated and got access to "WinYourLottery" from BobP.  Great information!  Some of the information contains odds calculations.  I need some help understanding how some of the numbers are calculated.

Using the following assumption that I wheeled 12 numbers

Odds of winning a prize when winning numbers are among your 12
5 if 5 among 12 = 1 in 792.00
4 if 4 among 12 = 1 in 99.00
4 if 5 among 12 = 1 in 22.63
3 if 3 among 12 = 1 in 22.00
3 if 4 among 12 = 1 in 7.07
3 if 5 among 12 = 1 in 3.77

I understand the following:

5 if 5 among 12 = 1 in 792.00 is calculated by (12!) / ( (7!) * (5!) ) which equals 792  or C(12, 5)

4 if 4 among 12 = 1 in 99.00 is calculated by (12!)  / ( (8!) * (4!) * 5) ) which equals 99 or C(12,4) / C(5,4)

3 if 3 among 12 = 1 in 22.00 is caculated by (12!) / ( (9!) * (3!) * 10) ) which equals 22 or C(12,3) / C(5,3)

But I have no idea how the 4 if 5, 3 if 4 or 3 if 5 odds are calculated.

Can someone help me with the math and how they are computed?

Jimmy

    jimjwright's avatar - Yellow 3.png
    Park City, UT
    United States
    Member #69864
    January 18, 2009
    993 Posts
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    Posted: February 7, 2009, 5:05 pm - IP Logged

    Never mind I think I figured it out.

    4 if 5 among 12 = C(12,5) / ( C(5,4) * C(7,1) ) = 792 / (5 * 7) = 22.63

    3 if 5 among 12 = C(12,5) / ( C(5,3) * C(7,2) ) = 792 / (10 * 21) = 3.77

    3 if 4 among 12 = C(12,4) / ( C(5,3) * C(7,1) ) = 495 / (10 * 7) = 7.07

     

    Jimmy

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      St-A-R
      Canada
      Member #51908
      May 1, 2007
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      Posted: February 9, 2009, 9:43 am - IP Logged

      The simple formula is like : Total numbers you want to play= x! / total numbers composing your bet
      For instance:
      Here the total number you want to play is  (12) and wish to make bet of 6 numbers, the calcul will be:

      12x11x10x9x8x7       
                         ____________________=    924    so it means  1 chance among  924 possibilities with
                           6x5x4x3x2x1                                  one combination or ticket.

      For instance: one combination of 6 numbers with the 6/49  means :

      (49x48x47)(46x45x44)
                          ________________     =    110,544  x  91,080
                            6x5x4x3x2x1                     _______________  =  1 / 13,983,816 
                                                                               720

      And so on..

      Hope it will help you to calcul !

      Rayal