There are 1000 red, orange and green t-shirts. We need to arrange them such that red orange pair can be a max of 25, red green pair can be a max of 15, orange red pair can be a max of 20, orange green pair can be max of 10, green red pair can be a max of 5, green orange pair can be a max of 22. The order matters. We need to arrange all 1000 tshirts in a horizontal line (left to right). The pair count given above is the tshirts placed next to each other (left to right). We do not have the count of each colour t-shirt, we only have the total number of t-shirts. So how to calculate the order possibilities?
I’m not entirely sure if we can compute this with a simple formula, since there are many moving parts in this problem.
What we would need to do is figure out the different ways we can arrange these t-shirts in consecutive chunks of t-shirts (i.e.112 red shirts, followed by 150 red shirts) and then for each one use the formula for permutations with repetition (which would be 1000!/(r! * o! * g!) in this case. However, to solve it we would need to know the number of shirts of each color.