a) if the odd digits must occupy the odd places?

I get: 3 x 2 x 2 x 1 x 1 = 12 ways....which I believe is correct but I do not understand the next question......

b) if the odd digits and the even digits must both be in ascending order? I see soooo many different cases so do not know where to start.

My teacher told me that the answer is 10 but I do not understand how she got it.

Please help!!