10 indistinguishable oranges are placed into 3 different plates, allowing some plates to be empty. How many different ways are there to do this? 

Putting the above text into English, please keep the original text's line breaks and format, and output the translation result directly.
【Analysis and Solution】
Counting, the method of inserting boards.
"Putting 10 indistinguishable oranges into 3 different plates, allowing some plates to be empty" is equivalent to "putting $10+3=13$ indistinguishable oranges into 3 different plates, with each plate having at least one orange"; there are $13-1=12$ gaps between the 13 indistinguishable oranges, and 2 boards are needed to place them into 3 different plates; as shown in the figure, the first plate has 2 oranges, the second plate has 7 oranges, and the third plate has 4 oranges; in total, there are $C_{12}^{2}=\frac{12 \times 11}{2 \times 1}=66$ different ways to place them.