hello, this is my first post. Nice meet you all.

To the point, I have encountered this problem on the GMAT resources>Advanced GMAT math topics> Advanced GMAT math questions

pg 23 question 1.
If there are 16 people to choose from, what is the ratio of the number of possible 7-person committees to the number of possible 8-person committees?
a.7:8
b.8:7
c.7:9
d.8:9
e.9:8

I was wondering if I solved this correctly or not, please view below.
[spoiler]identical question is discussed here (except for numbers)>https://www.beatthegmat.com/ratio-of-members-t19948.html

While I understand the reasoning discussed in the above, I was curious as how to answer it without using a calculator.

For this question answer would be 16C7:16C8,
so this would be 16!/7!9! : 16!/8!8!
then I would cancel things and be left with 1/9 :1/8 then cross flip (I don't know the proper term) 'em to get 8:9 right?[/spoiler]

Thank you