i got this.

There are five odd digits and four even digits to be used. Because the digits must alternate between odd and even, this means that there is only one possible way to distribute odds (O) and evens (E): OEOEOEOEO. Now, there are 5! =120 ways to arrange the odd numbers, as there are five choices for the first slot, four for the second, and so on. Similarly, there are 4!=24 ways to arrange the even numbers. Our final answer is the product of 120 and 24, which is **2880**.

And i find this logic clearer, Why?