Chapter 17, Problem 17.4E

Interpretation Introduction

Interpretation:

The value of $N!$ is to be expressed as a power of $10$ as well as power of $e$.

Concept introduction:

Combination formula is a possible way of grouping distinguishable objects into various subsystems. The equation for combination formula is as follows:

$C=\frac{N!}{\underset{i=1}{\overset{m}{\prod n_i!}}}$

Where,

• $N$ is the object.

If the value of $N$ is large, then the Stirling’s approximation method is used to estimate factorials. The Stirling’s approximation for large value of $N$ is,

$\ln N!\approx N\ln N-N$