This problem is a disguised version of the following question: if you have pick any 6 consecutive integers, what are the odds that two of them are divisible by 5? It's good to know that every fifth integer is divisible by 5, every 7th divisible by 7, etc.
Why is this so? If we're trying to find the odds that two are divisible by 5, we could select some groups of 6 integers and see what happens:
123456
234567
345678
456789
5678910
Notice every set of integers has one 5 in it, but in the last set, if we start with a 5, we'll end on a 10, giving us two integers divisible by 5. If we scoot one over again we'll lose the 5 and have a 10 in its place for the next 4 sets. Long story short, every fifth group has two numbers divisible by 5. Let's apply it to this problem:
BRGYBB
RGYBBR
GYBBRG
YBBRGY
BBRGYB
Since these are the only 5 ways you can select 6 cars in this order, and since only one has a red car twice, the answer is 1/5, or B.
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