Problem:
What is the product of all positive odd integers less than 10,000 ?
Answer Choices:
A. (5000!)210000!​
B. 2500010000!​
C. 250009999!​
D. 25000⋅5000!10000!​
E. 250005000!​
Solution:
Note that
1⋅3⋯9999=2⋅4⋯100001⋅2⋅3⋯9999⋅10000​=25000⋅1⋅2⋯500010000!​=25000⋅5000!10000!​​
The problems on this page are the property of the MAA's American Mathematics Competitions