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: , BWBW|BWBW, and WWW|BBW. How many different arrangements are there?

There are 362,880 different arrangements.

Step-by-step explanation:

Arrangements of n elements:

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

In this question:

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

How many different arrangements are there?

There are 362,880 different arrangements.

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b

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step-by-step explanation: