Calculating the Chances of a Particular Random Arrangement

The number of possible arrangements of a given number of objects increases dramatically with the addition of more objects. In fact, the numbers can be so staggering, we show on this page why the mathematical formula for determining the number of arrangements is accurate.

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. They are:

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 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. 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.

The number of possible arrangements of 20 cards is 1x2x3x4x5x6...x20 = 2,432,902,008,176,640,000.

So the chances of accidentally dealing 20 cards in one particular 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 or other necessary molecule? That number, whatever it is, is the reason why it did not happen by accident.

With each successive object, the number of possible arrangements increases exponentially. As the number of possible arrangements increases, the chance of randomly finding the right arrangement becomes more slim.

For instance, the chances of randomly finding a particular arrangement of 5 components in an enzyme is 1 in 120 - far from impossible given the number of generations claimed by evolution. But chances of striking the right arrangement for 8 components is 1 in 40,320.

So, if these arrangements were random mutations, as claimed by evolution, the chances of one accidental arrangement being the "right" arrangement of 8 cards is 1 in 40,320. The formula is 1x2x3x4x5x6x7x8=
40,320.

With 9 cards the chances are 1 in 362,880;

With 10 it is 1 in 3,628,800;

With 11 it is 1 in 39,916,800;

With 12 it is 1 in 479,001,600;

With 13 it is 1 in 6,227,020,800;

With 14, it is 1 in 87,178,291,200;

With 15 it is 1 in 1,307,674,368,000;

. . .

With 20 cards, the chances are 1 in 2,432,902,008,176,640,000.

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.

Of course, 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 impossibility is 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.