Yes this is possible to create a carousel like this with views.
Given that you've mentioned that it will be a Post Slider then i'm correct to assume that each slide in the slider is a separate post. If so then follow the instructions below:
1. Create your view by going to Toolset -> Views and click add new, then select the option "Display the results as a slider".
2. Using the Post Type setting on the view select the Post type that the slider will be displaying.
3. Under the "Pagination and Sliders Settings" you will change the setting to Display X number of items per page where x is the number of individual posts in the slide.
4. Also from the "Pagination and Sliders Settings" you can setup the transition types, etc
5. The Pagination Controls can be added using the Pagination Controls button in the Loop Editor section of the view.
6. I recommend using the Loop wizard to setup your column type layout using the Bootstrap columns and setting it to the same number of columns that you've listen in the Post per page.
Please let me know if this helps or if further clarification is needed.
