array of Weighted random numbers with constant sum

Is there any well-known algorithm which can generate an array of weighted random numbers having the same constant sum?

This problem can be stated in another way: Say, I have a total value of 20. Which should be distributed into 3 parts each of them has a weight of 2,4,3 respectively. So, I need 3 random numbers which will have a sum of 20 but the distribution will follow the weight.