First, the factors of 30 must be determined. These are 1, 2, 3, 5, 6, 10, 15, and 30. However, since there are only 3 people and we need the product of the numbers of items each person receives to be 30, the highest number of factors we can choose at a time is 3.

We can distribute the items in following methods:

(1, 1, 30), (1, 2, 15), (1, 3, 10), (1, 5, 6), (2, 3, 5)

That being said, order doesn`t matter in this question, meaning (1, 1, 30) is considered the same as (1, 30, 1) and (30, 1, 1). Therefore, option 3: `27` is incorrect as it over-counts the permutations.

Hence, there are 5 ways to distribute the items among the people so the product of the quantities each person receives is 30. But none of the provided options match the correct answer.

Alert - correct answer should be 5.