Enable the Item Count for SharePoint 2010 Search Refiner

In SharePoint 2010 you can modify the search refiner's xml text to show count on each category, the links listed at below which show you step-by-step for configure the refiner webpart.

http://www.sharepointanalysthq.com/2010/06/showing-items-counts-in-sharepoint-2010-search-refiners/ or http://httpcode.com/blogs/PermaLink,guid,935719ed-8d5d-4206-b7e9-de1c2dd72f65.aspx.

But one thing have to bear in mind the SharePoint 2010 item count does not same as Fast Search for SharePoint's deep refiner, the SharePoint item count will shown only 50 items by default and hard limit to 500 items. What this mean is the item count will not go beyond  limit even if search results have more than 500, the system only update counting when user select next page or next result set.

As told by relevant personnel who work in Microsoft, it is because of SharePoint search index not same as Fast Search advance index algorithm. 

Fast Search for SharePoint 2010's Document Preview is not working

There are number of issues which might causing Fast's Document Preview failed to work, if one of these points is met.

1) Silverlight is not installed on machine which search performed.
Go to http://www.silverlight.net/ and download Silverlight runtime.

2) The Office Web Application for SharePoint 2010 is not installed.
Technet's step-by-step to deploy the Office Web App, http://technet.microsoft.com/library/ff431687(office.14).aspx.

3)  Without run the SharePoint Configuration Wizard after setup the Office Web Application for SharePoint 2010.
Run the SharePoint Products and Technologies Configuration Wizard on each SharePoint server in server farm.

4) Search results can be returned but "401 unauthorized" message occurred on Document Preview's ajax callback to server.
This might because of the loopback issue on SharePoint server's IIS, click here for details of how to disable loopback check on Windows Server.