How many ways can 64 be divided into 10?

Answer 1

The number of ways to divide 64 into 10 parts depends on whether we allow the parts to be equal or if they must be distinct. If we are considering the number of non-negative integer solutions to the equation ( x_1 + x_2 + \ldots + x_{10} = 64 ), we can use the "stars and bars" theorem, which gives us (\binom{64 + 10 - 1}{10 - 1} = \binom{73}{9}). Thus, there are 73 choose 9 ways to divide 64 into 10 non-negative parts.