How many ways are there to place 10 indistinguishable balls into eight distinguishable boxes?

The problem of placing 10 indistinguishable balls into 8 distinguishable boxes can be solved using the "stars and bars" combinatorial method. The formula for this is given by (\binom{n+k-1}{k-1}), where (n) is the number of balls and (k) is the number of boxes. Here, (n = 10) and (k = 8), so the number of ways is (\binom{10 + 8 - 1}{8 - 1} = \binom{17}{7} = 19448). Thus, there are 19,448 ways to place the balls into the boxes.