In order to use this for chemical species that often have Avogadro's number of particles present, we employ Stirling's Approximation. Stirling's Approximation is useful for large numbers on the order of Avogadro's number. But the approximation fails for small numbers. Determine where the use of Stirling's approximation is appropriate. You should consider and explain what your tolerance for error is along with a value of N (number of objects) above which the approximation is valid. Use any mathematical device you deem appropriate.