sql server count of max values without subquery

Question

I want to write a T-SQL query which returns not only the maximum value, but the number of rows having the maximum value. There must be a better way than what I have come up with

 --wrong way 
 select LibraryBranchId, max(daysCheckedOut), count(daysCheckedOut) 
 from books group by LibraryBranchId

 LibraryBranchId   Expr1      Expr2
 ----------------------------------
 1                 100       398503  (WRONG!)
 2                 75         94303  (WRONG!)
 3                 120       103950  (WRONG!)

I can do this correctly by INNER JOINing a subquery but it seems wasteful

 --right way, but seems WAY too long
 select LibraryBranchId,max(daysCheckedOut),count(daysCheckedOut)
 from books inner join 
   ( select LibraryBranchId, max(daysCheckedOut) as maxDaysCheckedOut
     from books group by LibraryBranchId ) as maxbooks 
 on books.LibraryBranchId=maxbooks.LibraryBranchId
 where daysCheckedOut=maxDaysCheckedOut
 group by LibraryBranchId 

 LibraryBranchId   Expr1      Expr2
 ----------------------------------
 1                 100           17  (RIGHT!)
 2                 75            11  (RIGHT!)
 3                 120            2  (RIGHT!)

So is there a way that is as simple as query #1, but returns the correct result as in query #2?

MS SQL Server 2000

EDIT: I missed two important GROUP BYs above on my first try at entering this, I have added them EDIT: Pretend that the version that Cade Roux wrote is what I wrote

Solution

I think that's right:

SELECT maxbooks.LibraryBranchId, maxbooks.maxDaysCheckedOut, count(*)
FROM books
INNER JOIN (
    SELECT LibraryBranchId, max(daysCheckedOut) AS maxDaysCheckedOut
    FROM books
    GROUP BY LibraryBranchId
) AS maxbooks
    ON books.LibraryBranchId = maxbooks.LibraryBranchId
    AND books.daysCheckedOut = maxbooks.maxDaysCheckedOut
GROUP BY maxbooks.LibraryBranchId, maxbooks.maxDaysCheckedOut

I don't think there's a simpler way - conceptually, it's the intersection of two sets. The set of tuples about the branches and the set of tupes satisfying that.