Warning! 
Alan's solution is incorrect because 
he used 10×10 or 100 for the number 
of choices for the side dishes. This 
counts selecting, say, corn first and 
slaw second as different from selecting
slaw first and corn second, when they 
are the same choice.  That's why his
answer is too large.

Edwin's solution:

Number of ways to choose the main course, (which is 5)

AND (TIMES)

Number of ways to choose the side dishes:

  A.  Number of ways to choose two different side dishes, 10C2
  
  OR (PLUS)
  
  B.  Number of ways to choose the same side dish twice, 10

AND (TIMES)

Number of ways to choose the dessert 

That's 









Edwin