- #1

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*In how many ways can the digits 1 through 9 be arranged such that*

Well I don't really have a good idea on how to solve this.

If we start with the scenario:

2 4 6 8 _ _ _ _ _ there are 5! arrangements

We could also shift the 2 4 6 8 block five times and still have them in ascending order.

Also we could shift the 8 in 6 ways, so that:

2 4 6 remains fixed and we would have 6! ways for the other numbers to be arranged, but we would count the scenario with 8 in the fourth place twice.

After that it gets a little more difficult. If I fix the 2 and 4 in the first two places, how many arrangements can I make so that the 6 is in front of the 8?

Also is there an easier way to solve this?

*In how many ways can the digits 1 through 9 be arranged such that the even digits appear in ascending order?*

Well I don't really have a good idea on how to solve this.

If we start with the scenario:

2 4 6 8 _ _ _ _ _ there are 5! arrangements

We could also shift the 2 4 6 8 block five times and still have them in ascending order.

Also we could shift the 8 in 6 ways, so that:

2 4 6 remains fixed and we would have 6! ways for the other numbers to be arranged, but we would count the scenario with 8 in the fourth place twice.

After that it gets a little more difficult. If I fix the 2 and 4 in the first two places, how many arrangements can I make so that the 6 is in front of the 8?

Also is there an easier way to solve this?