Factorials and lists/subsets counting

[reenmachine]

1.1 Homework Statement

Using only pencil and paper , find the value of $\frac{120!}{118!}$

2.1 Relevant equations

$\frac{120 \cdot 119 \cdot 118!}{118!} = 120 \cdot 119 = 14280$

1.2 Homework Statement

Compute how many 9-digit numbers can be made from the digits 1,2,3,4,5,6,7,8,9 if repetition is not allowed and all the odd digits occur first (on the left) followed by all the even digits (i.e. as in 1375980264 but not 0123456789).

(this question is from a book so I have no clue why they included 0 in their exemples , so I will just ignore it and take for granted that it's a mistake)

2.2 Relevant equations

My guess is this is like doing two different lists , one for the odd numbers and one for the even numbers.

The formula I intuitively came up with is $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ which in retrospective is simply $5!4! = 2880$.

Any thoughts on those two problems and my attempt at solving them?

Thanks!

 

[haruspex]

All looks right.

 

[reenmachine]

thank you!