Random numbers from specific range with fixed sum in Excel

I want to create a number of random columns in Excel with those characteristics:

• Each column has 9 cells
• Each cell is either 1, 2, or 3
• Each column has SUM = 10

I tried creating 9 random numbers in column A and then use ROUND(B1/SUM(B$1:B$9);1)*10 for the columns but due to ROUND (I think) it is not completely correct as not all columns have sum=10 (some have 8 others 10 e.t.c.)