Scheme: Math Kangaroo Contest 2013

It was really nice question at Math Kangaroo Contest 2013

Four cars enter a roundabout at the same time, each one from a different
direction, as shown in the diagram. Each of the cars drives less than a full
round of the roundabout, and no two cars leave the roundabout in the
same direction. How many different ways are there for the cars to leave
the roundabout? 

I would like to introduce elegant solution in scheme

(let ([src '(A B C D)])
 (length ( filter-not
           (lambda(x)
             (ormap eq? x src))
           (permutations src)) )
  
)

So you can find correct answer for four cars (9) , five cars (44) and more

Enjoy!