If I expand 25*24*23* ... *12*11*10, how many zeros are there at the end of the number I get?
+9519 10 * 11 * 12 * ... * 25 = (10 * 15 * 20 * 25) * (other numbers)
The other numbers don't have any factor of 5. We consider 10 * 15 * 20 * 25.
10 * 15 * 20 * 25 = 5^5 * 2^3 * 3
Pick two even numbers from (other numbers) to make 5^5 * 2^5 = 10^5.
There will be 5 zeros at the end.
