Hey, I noticed that you helped a lot of people with permutation and combination problems. I need your assistance.
I need to figure out this permutation/combination formula. How do I add the rule that objects within a particular set obey a hierarchy (i.e., the already predefined list of objects follows the rule that one object cannot appear below another object when it was originally listed above the object).
To better express my meaning clearly, here’s an example:
Set #1 - James, Jennifer, Jason, Amber
In the permuted/combinated list, James shall always appear above Jason and Amber. Amber shall always appear below Jennifer.
I want to add that rule, but I don’t know how.
Furthermore, I want to define this rule for more than one set. I want an equation that will permute/combinate different rules for different sets, but render all possible patterns based on those rules. Each set has 10 items, so the third set will contain only 10 items.
For simplicity sake, I’ll keep the number of items in the list down to six:
Ex. Set #1 - James, Jennifer, Jason, Amber, Florence, Carrie
Ex. Set #2 - Dustin, Michael, Morgan, Lance, Travis, Patrick
The rules are that names will be selected based on a preset pattern (i.e., names will be selected in a 4-6, 5-5, or 6-4 manner). For the first equation, each set maintains their respective hierarchy, but the hierarchy for set #2 does not apply to the hierarchy of set #1. Basically, 4 names will be randomly selected from set #1 and 6 names will be randomly from set #2, 5 names from both, and then 6 names and then 4 names. Once the formula/program solves the permutations/combinations, I want it to take those results and decipher the third set–in essence, match the results against the given but unknown information of the third set.
The third set will have numbers: 2, 2, 1, 3, 3, 4
Each individual in each set will have a rank designation.
Ex. Set #1 - James 2, Jennifer 3, Jason 4, Amber 1, Florence 1, Carrie 2
Ex. Set #2 - Dustin 1, Michael 3, Morgan 2, Lance 3, Travis 1, Patrick 2
Based on given information from the third set, the formula or program will most likely suggest a possible combination that suits the (2, 2, 1, 3, 3, 4) parameter:
James 2, Morgan 2, Amber 1, Michael 3, Jennifer 3, Jason 4
I’m no mathematician, but here’s how I visualize the equation in Microsoft Excel or something:
[(~set #1 & #2 - 4/6)(~set #1 & #2 - 5/5)(~set #1 & #2 - 6/4)] | (set #3)
** Please note that the selection process requires that both sets have 10 items (e.g., 4 items will be selected from set #1’s list of 10 items, 6 items will be selected from set #2’s list of 10 items). Under the aforementioned precepts, this “equation” represents all possible arrangements for these individuals. Then it matches those results and “deciphers” set #3.
I want to do this in excel or in another program, but I don’t know how to manipulate the permutation/combination formulas to obey new rules and so forth. I need help developing a workable formula.
