How many ways are there to put 4 balls in 3 boxes if the balls are not distinguishable but the boxes are?

Please give me the correct answer

tooo many wrong answers today

You can divide into cases:

4-0-0: 3 ways 3-1-0: 3 x 2 = 6 ways 2-2-0: 3 x 2 = 6 ways 1-1-2: 3! = 6 ways

Total is then 3 + 6 + 6 + 6 = 21 ways.