Help With Visualforce Page

I could use some help on a Visualforce page, assuming this is possible.

We have a simple Visualforce page coded as follows:

<apex:page standardController="Case" showHeader="false" sidebar="false">

     <c:CaseCommentsComponent CurrentCaseId="{!Case.Id}"/> 

</apex:page>

I know that I can put an If statement into the above code - for example:

{! IF(Case.Status = "Closed", "Sorry Case is Closed", "Case is Open") }

This displays the hard-coded text according to the status of the case.  But what I would like to do is call one Visualforce component if the case is closed and a different component if the case is open.  Is it possible to do this?  Something like the following (although I know this doesn't work as coded)?

<apex:page standardController="Case" showHeader="false" sidebar="false">     

{! IF(Case.Status = "Closed", <c:ClosedCaseCommentsComponent CurrentCaseId="{!Case.Id}"/>, <c:CaseCommentsComponent CurrentCaseId="{!Case.Id}"/>) } 

</apex:page>

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