AMC 10 Weekly Practice Round 3

This problem is equivalent to placing identical balls into distinct boxes, allowing some boxes to be empty.

Arrange the balls in a row and use dividers to separate them into groups. Since empty boxes are allowed, dividers may be adjacent. Assign the first, second, third, and fourth groups to the variables respectively.

Because the balls are identical and the dividers are also identical, this is equivalent to arranging balls and dividers in a line. The number of such arrangements is

Therefore, the answer is .