Question

This problem uses the statistical postulate to address diffusion. Consider eight particles, 4 black and 4 white. The particles are in a liquid with two halves separated by a permeable membrane, so each particle can be either on the left or the right of the membrane. According to the statistical postulate, every arrangement of the 8 particles is equally likely. Arrangements can be summarized according to which particles are on the left and which on the right, with the membrane represented by a vertical line |. Some possible arrangements are: BBBBWWWW, BWBW|BWBW, and WWW|BBW. How many different arrangements are there?

Answer 1

There are 362,880 different arrangements.

Explanation:

Arrangements of n elements:

The number of possible arrangements of n elements is given by:

`A_(n) = n!`

In this question:

Arrangements of 8 particles, plus the membrane, for which there are 9 possible positivos.

How many different arrangements are there?

`T = 9A_(8) = 9*8! = 362880`

There are 362,880 different arrangements.