Seeing helicoptor captures of car packed streets, and the sort order of colors can be observed, if for simplicity we limit the scope of the pictures to say 9 or 10 cars, I wondered whether it is possible to count all the unique arrangements of the 9 colored cars in a line (assuming we have 4 blue and 5 green ones) where the order g..g..b..g..b can always be found in the arrangement. That is, an order involving only 5 cars is sought for out of the 9.
I have a feeling it is very similar to introductory problems in probability involving a bowl of colored balls, where we know how the bowl is composed, and we are asked how many arrangements of this and that color can be observed in order, if we pick a number of balls at a time.
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