I have a list of n objects
say [ apple, orange, carrot, cherry, banana ]
Now I am trying to come up with an equation which will generate an unique number for each combinations from this list.
say I assign following values for each items
apple = 1 orange = 2 carrot = 3 cherry = 4 banana = 5
If I directly add the individual values to generate combination score then the values will be
apple = 1 apple, carrot = 4 apple, orange = 3
But here multiple combination can have same scores.
I need to generate an equation which will generate UNIQUE score for all of these combination.
POSITION IS NOT AN ISSUE.
Score(apple,orange,carrot) = Score(carrot, apple, orange) = Score (orange, apple, carrot)
But Score (apple, carrot) $\ne$ Score(cherry)
How this can be generated ?