Detailed Instructions: Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.
Q: Problem: in a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. no other points are awarded. john participated several times in the competition and finished first, second, third, or fourth each time. the product of all the points he received was 38500. how many times did he participate in the competition ?
Options: a. 6, b. 7, c. 8, d. 9, e. 10
A:
b