Pauline’s Pastries is making special petit fours (as in problem 12-78). The chef is making petit fours with three or four fillings. For Valentine’s Day they have twelve fillings available and they make one petit four for each of the possible three or four different fillings.

1. How many petit fours did they make?

   Hint (a):

   Does order matter?

   More Help (a):

   Set up a combination equation. If you need help, refer to the Math Notes box in Lesson 12.1.4.

   Answer (a):

   $_{12}C_{4}+_{12}C_{3}=715$

2. What is the probability of getting a petit four that has both raspberry and custard?

   Hint (b):

   If raspberry and custard are known filling, then there are two fewer fillings to choose from.