We are seeing that computing combinations and permutations involves the n! (factorials) function, which increases very rapidly as n increases. For example, the formula for the number of combinations of m objects taken from a group of n objects is giving by:

n! / m!(n - m)!

But there is a way to deal with these very high values that usually does not require the use of a calculator. For example:

40! / (3!(40 - 3)!).

40! is a very large number having 47 places, but how can the above computation be done very easily without the use of a calculator?