**On a table there are 10 different objects that can be colored using 5 different colors**

**a) How many ways can the 10 objects be colored?** $10 \choose 5$

**b) How many ways can the 10 objects be colored using all different colors?** $5! \cdot 5!$ because I have to order 5 colors in 10 places, but when 5 places are "colored" I have 5 more place to color.

**c) How many ways can the 10 objects be colored in such a way that each color is used at most 3 times?** any idea?

Are my first two solutions right? what's about the third question? maybe $ 10 \choose 5 $ - $10 \choose 2$?