There are six clearly distinguishable frogs sitting in a row. Two are green, three are red, and one is blue. Green frogs refuse to sit next to the red frogs, for they are highly poisonous. In how many ways can the frogs be arranged?
without being able to distinguish individual frogs we only have 2 possible orderings
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Now if you say we are able to uniquely identify each frog then we have 2!=2 ways of arranging the green frogs and 3!=6 ways of arranging the red frogs. So there are a total of 2*2*6 = 24 ways of arranging the frogs to their liking.