Chapter 17, Problem 17.5E

Interpretation Introduction

(a)

Interpretation:

By using Stirling’s approximation, the value of $6.02\times {10}^{23}!$ is to be estimated.

Concept introduction:

Combination formula is a possible way of grouping of 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,

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

Interpretation Introduction

(b)

Interpretation:

By using Stirling’s approximation, ${10}^{100}!$ is to be estimated.

Concept introduction:

Combination formula is a possible way of grouping of 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,

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