10. Compute

If we use the method that puts 5 consecutive factors on the top and bottom of a fraction starting with a 25 on top and a 5 on the bottom, we get,

The bottom will entirely cancel.

If we use the factorial method we get

and we see the effect of round off error in our calculation. If you have your calculator do the computation with the factorials, it will work with more places than it shows you so that the round off error will be in places that are beyond what you see, and it will actually give you the correct answer. In this case, I punched in the numbers the calculator gave me for the factorials and had the calculator divide with the punched in numbers. It came out very close to what it should have but it was off by the smallest amount.