I'm working on some homework right now, and I've gotten stumped. Here's the question I'm on:
How many of the 9000 four-digit integers 1000, 1001, 1002, . . . , 9998, 9999 have four distinct digits that are either increasing (as in 1347 and 6789) or decreasing (as in 6421 and 8653)?
Through some Googling I've already found what they answer may be, but I have no idea how to arrive at the answer, so I wouldn't be learning anything from this hurdle like I'm supposed to. I can use all the help I can get on this one since I don't even know where to start. I think I have to apply the formula for permutations to this somehow, but I don't know what adjustments I have to make for it to work right.