lele22141 lele22141

19-03-2021
Mathematics

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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?

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joaobezerra joaobezerra

21-03-2021

Answer:

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:

[tex]A_{n} = n![/tex]

In this question:

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

How many different arrangements are there?

[tex]T = 9A_{8} = 9*8! = 362880[/tex]

There are 362,880 different arrangements.

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