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Combination Formula with a lockout twist

  1. Nov 12, 2011 #1
    Combination Formula with a "lockout" twist

    Hi! I am trying to figure out all possible combonations for 6 items among a group of 18 choices. So I turn to my old friend C(n,r) to calculate where n=18 and r=6. "But WAIT!" I tell you before you hastily begin scribbling, "There is a twist..." You see my problem is that the items are divided up into 6 groups, with 3 choices in each group. Once a choice has been made in a group for the combination the other 2 in the group are unavailable, or "locked out" of the rest of the combination. The order doesn't necessarily matter but a choice must be selected from each of the six groups. Here's a visual representation:

    A B C
    1 A1 B1 C1
    2 A2 B2 C2
    3 A3 B3 C3
    4 A4 B4 C4
    5 A5 B5 C5
    6 A6 B6 C6

    If "B1" is selected in a single combination then "A1" and "C1" cannot be apart of the same combination. What is the formula for this and how many possible combinations are there?
     
  2. jcsd
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