Calculate the number of ways of choosing three molecules from a collection of six molecules.

Question

Accepted Answer

Using Eq. (8.3), the number of ways of choosing three molecules from a collection of six molecules is equal to

[latex]\left(\begin{matrix} N \n\end{matrix} ight)=\frac{N!}{n!(N − n)!} .[/latex] (8.3)

[latex]\left(\begin{matrix} 6 \3 \end{matrix} ight)=\frac{6!}{3!3!}=\frac{1 · 2 · 3 · 4 · 5 · 6}{(1 · 2 · 3)(1 · 2 · 3)} = 4 · 5 = 20.[/latex]

There are thus 20 ways of choosing the three molecules, which is consistent with the appropriate entry in the fourth row of
Table 8.2.

TABLE 8.2 Possible distributions of six molecules between two compartments.
Distributions		Weights	Probabilities
[latex]n_{a}[/latex]	[latex]n_{b}[/latex]	W	P
0	6	1	1/64
1	5	6	6/64
2	4	15	15/64
3	3	20	20/64
4	2	15	15/64
5	1	6	6/64
6	0	1	1/64
		64	1

Question 8.1: Calculate the number of ways of choosing three molecules fro...