Problem number 19. Hermione, Harry, and Ron always walk into the common room one at a time. Hermione is never first, Harry is never second, and Ron is never third. In how many different orders could they walk in? To solve this problem, let's make a chart as to who could be first, who could be second, and who could be third. And let's start with the first statement. Hermione is never first. So we can't have Hermione here, but she could be second. Harry is never second, so possibly he could be first or third, and Ron is never third, so Ron cannot be in this spot. So if Hermione is second, Ron could only be first. Harry would be third. And because we can't switch Ron and Harry here, because Ron can't be third, this is the only way that they can walk in if Hermione is second. Now Hermione could be third. Let's see what would happen then. Harry can't be second, so he will have to be first. And Ron can't be third, so he could be second. And again, we cannot switch these because Harry cannot be second. So this is the only order that they could walk in if Hermione is third. So since Hermione can't be first, and there's only one order when she's second, and only one order for them to walk in when she's third, there are only two possible orders in which they could walk in. Answer is B.

Hermione

Harry

Ron

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