To solve this problem, we need to distribute 9 pies among 3 people such that each person receives an odd number of pies. The possible distributions of odd numbers that sum to 9 are (1, 1, 7), (1, 3, 5), and (3, 3, 3).

1. For the distribution (1, 1, 7):

Choose 1 pie for the first person: \(\binom{9}{1}\)

Choose 1 pie for the second person from the remaining 8 pies: \(\binom{8}{1}\)

The third person gets the remaining 7 pies: \(\binom{7}{7}\)

Since the people are distinct, multiply by the number of ways to assign these distributions: \(\binom{3}{1}\)

Total ways for (1, 1, 7) = \(9 \times 8 \times 1 \times 3 = 216\)

2. For the distribution (1, 3, 5):

Choose 1 pie for the first person: \(\binom{9}{1}\)

Choose 3 pies for the second person from the remaining 8 pies: \(\binom{8}{3}\)

The third person gets the remaining 5 pies: \(\binom{5}{5}\)

Since the people are distinct, multiply by the number of ways to assign these distributions: \(3!\)

Total ways for (1, 3, 5) = \(9 \times 56 \times 1 \times 6 = 3024\)

3. For the distribution (3, 3, 3):

Choose 3 pies for the first person: \(\binom{9}{3}\)

Choose 3 pies for the second person from the remaining 6 pies: \(\binom{6}{3}\)

The third person gets the remaining 3 pies: \(\binom{3}{3}\)

Total ways for (3, 3, 3) = \(84 \times 20 \times 1 = 1680\)

Adding all the possibilities: \(216 + 3024 + 1680 = 4920\)