Calculating the Chances of a Particular Random Arrangement

The chance arrangement of a particular things (like molecules or atoms) is crucial to the theory of evolution because the core of the theory is the belief that everything occurred through random chance with environmental stresses removing the less perfect. So what are the chances that the molecules in a particular protein, for instance, accidentally came together in the right configuration to produce a superior protein or a superior animal?

The answer to this question is a mathematical formula, a well worn, simple and universally accepted formula.

The formula to determine how many possible arrangements there are for a given number of objects is to multiply progressive numbers from 1 to the number of objects.

For instance, the mathematical formula to determine how many possible arrangements there are for two cards is 1x2=2. There are two possible arrangements of two cards. They are:

A K

K A

The formula for the number of possible arrangements of 3 cards is 1x2x3=6 because with the addition of the third card there are three times as many combinations as before. So, there are 6 possible arrangements for three cards. They are:

A K Q

A Q K

K A Q

K Q A

Q A K

Q K A

The formula for the number of possible arrangements of 4 cards is 1x2x3x4=24. So, there are 24 possible arrangements of 4 cards because with the addition of the 4th card, there are 4 times as many different arrangements as before. That means there is a 1 in 24 chance that a random arrangement of four cards would be the correct arrangement:

A K Q J

A K J Q

A Q K J

A Q J K

A J K Q

A J Q K

K A Q J

K A J Q

K Q A J

K Q J A

K J A Q

K J Q A

Q A K J

Q A J K

Q K A J

Q K J A

Q J A K

Q J K A

J A K Q

J A Q K

J K A Q

J K Q A

J Q A K

J Q K A

The actual arrangements are placed on this page because, as will later be seen, when more that just several numbers are in play, the results are staggering.

The formula for the number of possible arrangements of 5 cards is 1x2x3x4x5=120 because with the addition of the 5th card, there are 5 times as many arrangements than there were before. There are 120 possible arrangements of only 5 cards. That is one chance in 120 to obtain the correct the by a random shuffling. They are:

A K Q J 10

A K J Q 10

A Q K J 10

A Q J K 10

A J K Q 10

A J Q K 10

A K Q 10 J

A K J 10 Q

A Q K 10 J

A Q J 10 K

A J K 10 Q

A J Q 10 K

A K 10 Q J

A K 10 J Q

A Q 10 K J

A Q 10 J K

A J 10 K Q

A J 10 Q K

A 10 K Q J

A 10 K J Q

A 10 Q K J

A 10 Q J K

A 10 J K Q

A 10 J Q K

K A Q J 10

K A J Q 10

K Q A J 10

K Q J A 10

K J A Q 10

K J Q A 10

K A Q 10 J

K A J 10 Q

K Q A 10 J

K Q J 10 A

K J A 10 Q

K J Q 10 A

K A 10 Q J

K A 10 J Q

K Q 10 A J

K Q 10 J A

K J 10 A Q

K J 10 Q A

K 10 A Q J

K 10 A J Q

K 10 Q A J

K 10 Q J A

K 10 J A Q

K 10 J Q A

Q A K J 10

Q A J K 10

Q K A J 10

Q K J A 10

Q J A K 10

Q J K A 10

Q A K 10 J

Q A J 10 K

Q K A 10 J

Q K J 10 A

Q J A 10 K

Q J K 10 A

Q A 10 K J

Q A 10 J K

Q K 10 A J

Q K 10 J A

Q J 10 A K

Q J 10 K A

Q 10 A K J

Q 10 A J K

Q 10 K A J

Q 10 K J A

Q 10 J A K

Q 10 J K A

J A K Q 10

J A Q K 10

J K A Q 10

J K Q A 10

J Q A K 10

J Q K A 10

J A K 10 Q

J A Q 10 K

J K A 10 Q

J K Q 10 A

J Q A 10 K

J Q K 10 A

J A 10 K Q

J A 10 Q K

J K 10 A Q

J K 10 Q A

J Q 10 A K

J Q 10 K A

J 10 A K Q

J 10 A Q K

J 10 K A Q

J 10 K Q A

J 10 Q A K

J 10 Q K A

10 A K Q J

10 A Q K J

10 K A Q J

10 K Q A J

10 Q A K J

10 Q K A J

10 A K J Q

10 A Q J K

10 K A J Q

10 K Q J A

10 Q A J K

10 Q K J A

10 A J K Q

10 A J Q K

10 K J A Q

10 K J Q A

10 Q J A K

10 Q J K A

10 J A K Q

10 J A Q K

10 J K A Q

10 J K Q A

10 J Q A K

10 J Q K A

The formula for the number of possible arrangements of 6 cards is 1x2x3x4x5x6=720 because with the addition of the 6th card there are 6 times as many arrangements as there were with only 5 cards. So, just 6 cards can be arranged in 720 possible ways.

If we add 14 cards to the 6 cards we had (20 cards) the number becomes staggering. Try it yourself. The number of possible arrangements of 20 cards is 1x2x3x4x5x6...x20 = 2,432,902,008,176,640,000. The chances of accidentally dealing 20 cards in one particular order or the chances that 20 different molecules in an enzyme would come together in one particluar order is 1 in 2,432,902,008,176,640,000.

Given that, what are the chances of just 36 different enzymes being accidentally arranged in the correct order by chance mutations in order to create one necessary protein when each molecule of the protein must be correctly placed? That number, whatever it is, is the reason why it did not happen by accident.

There are only 1,051,200,000,000,000 seconds in two billion years. So, with the random combinations of just 20 cards, one has already surpassed the number of seconds in two billion years by more than two thousand times. That is, the number of random combinations of just 20 cards is more than two thousand times the number of seconds in two billion years.

Considering the formation of one enzyme, all components of the enzyme must be in place before it is of use. So, to form an enzyme that has 38 components, even if one had all of the components together and all of the components had already evolved properly, the chances of combining them by chance and hitting the correct arrangement is astronomical.

The same concepts hold true for the formation of the original organic protein in Darwin's primordial soup:

Life cannot have had a random beginning; The trouble is that there are about two thousand enzymes, and the chance of obtaining them all in a random trial is only one part in 10^{40,000}, an outrageously small probability that could not be faced even if the whole universe consisted of organic soup.

If one proceeds directly and straightforwardly in this matter, without being deflected by a fear of incurring the wrath of scientific opinion, one arrives at the conclusion that biomaterialists with their amazing measure of order must be the outcome of intelligent design. … problems of order, such as the sequences of amino acids in the chains … are precisely the problems that become easy once a directed intelligence enters the picture.

(Fred Hoyle & N. Chandra Wickramasinghe, Astronomers, Mathemeticians & Cosmologists, University College Cardiff, Evolution from Space, J. M. Dent & Sons 1981, and in The Omni Lecture, :And Other Papers on the Origin of Life, Enslow Publishers 1982, p. 27-28)

It was later discovered that there are at least 20,000 such enzymes.

Some chemicals can have certain alterations of the arrangement of their components and still be effective, but given the number of possible chances, the overall chances are hardly diminished.

This concept of chance (and chance is the core of the evolutionary theory), must also be applied no only to chemicals but also to things which, by definition, must have a precise arrangement, such as the arrangement of neurological connections in your brain or the appropriate components for a mathematical algorithm or the non-physical logic utilized by cells to communicate in code. On top of this one must consider that hundreds if not thousands of different such combinations must occur simultaneously ...

When one considers that there are 1,000,000,000,000,000 cards in the "deck" of neurological connections in a human brain, it is easy to see that it is simply impossible for them to have formed by means of random accidents. There is no name for such a number.