Combination Formula with a lockout twist

In summary, the conversation is about finding all possible combinations for 6 items from a group of 18 choices, with a twist where the items are divided into 6 groups and once one item is selected from a group, the other two are "locked out" of the rest of the combination. The formula for this problem and the number of possible combinations were also discussed.
  • #1
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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?
 
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  • #2
Try to start with a smaller problem (1,3) and (2,6) which you can count and then calculate this one. Honestly, I didn't quite understand the setup.
 

What is the "Combination Formula with a lockout twist"?

The "Combination Formula with a lockout twist" is a mathematical formula used to determine the number of possible combinations that can be created using a set of elements or objects, while also accounting for a lockout mechanism that restricts certain combinations from being used.

How is the Combination Formula calculated?

The Combination Formula is calculated using the formula: nCr = n! / (r!(n-r)!), where n represents the total number of objects and r represents the number of objects being chosen for each combination. This formula can be modified to include a lockout mechanism by subtracting the number of restricted combinations from the total number of combinations.

When should the Combination Formula with a lockout twist be used?

This formula should be used when there is a set of objects or elements and a lockout mechanism in place that restricts certain combinations from being used. It can be applied in various fields such as cryptography, game design, and statistical analysis.

Can the Combination Formula with a lockout twist be used for any type of lockout mechanism?

Yes, the Combination Formula can be used for any type of lockout mechanism as long as the number of restricted combinations is known. It can be used for lockout mechanisms such as pattern locks, password locks, and key-based locks.

How is the Combination Formula with a lockout twist useful in scientific research?

The Combination Formula with a lockout twist can be useful in scientific research for analyzing and understanding complex systems or processes. It can be used to determine the number of possible configurations or outcomes in a system, while also considering any restrictions or limitations. This can aid in making predictions and identifying patterns in data.

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