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The exponential decrease is illustrated by a simple example.  Suppose you were to put in a brown bag 26 upper case letters of the alphabet, 26 lower case letters and a period, space and a comma.  You now have all the possibilities in the bag necessary to write a coherent book.  What would be the likelihood of randomly pulling letters in the sequence necessary to spell the first word of the title of the book, which we will title DESIGN vs. Chance. Lets also assume that each time we pull a letter, we will return it to the bag after noting its occurrence? The chance of pulling the D is 1/55.  But to get “DE,” the first two letters in the necessary sequence, the chance is 1/55 times 1/55 or 1/3025.  To get three letters, DES, the probability is 1/55 x 1/55 x 1/55 = 1/166,375.  Four letters, DESI is 1/9,150,625.  Five, DESIG is 1/500 million and six, DESIGN is 1/28 billion.  
 
The exponential decrease is illustrated by a simple example.  Suppose you were to put in a brown bag 26 upper case letters of the alphabet, 26 lower case letters and a period, space and a comma.  You now have all the possibilities in the bag necessary to write a coherent book.  What would be the likelihood of randomly pulling letters in the sequence necessary to spell the first word of the title of the book, which we will title DESIGN vs. Chance. Lets also assume that each time we pull a letter, we will return it to the bag after noting its occurrence? The chance of pulling the D is 1/55.  But to get “DE,” the first two letters in the necessary sequence, the chance is 1/55 times 1/55 or 1/3025.  To get three letters, DES, the probability is 1/55 x 1/55 x 1/55 = 1/166,375.  Four letters, DESI is 1/9,150,625.  Five, DESIG is 1/500 million and six, DESIGN is 1/28 billion.  
 
 
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As one can see, chance may explain short sequences having low complexity.  However, chance cannot plausibly account for longer and longer sequences where the complexity also exhibits a purpose.  The exponential decrease in probability is a major problem for the explanatory power of any chance mechanism, even with a universe trillions of years old.  When one does the calculation one finds that even if every elemental particle in the entire universe was a monkey and all monkeys started banging away at typewriters with 55 keys at the rate of 1045 per second at the beginning of the big bang, they still would not have produced a specific sequence equivalent to the first sentence of Lincoln’s Gettysberg Address.  Because of the exponential decrease in probability, they would exhaust the available probability resources to get only the first 87 of the 175 letters and spaces that make up the sentence.  And the most simple DNA sequence is 100's of times more complex than the first sentence of the Gettysberg Address.
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As one can see, chance may explain short sequences having low complexity.  However, chance cannot plausibly account for longer and longer sequences where the complexity also exhibits a purpose.  The exponential decrease in probability is a major problem for the explanatory power of any chance mechanism, even with a universe trillions of years old.  When one does the calculation one finds that even if every elemental particle in the entire universe was a monkey and all monkeys started banging away at typewriters with 55 keys at the rate of 1045 per second at the beginning of the big bang, they still would not have produced a specific sequence equivalent to the first sentence of Lincoln’s Gettysburg Address.  Because of the exponential decrease in probability, they would exhaust the available probability resources to get only the first 87 of the 175 letters and spaces that make up the sentence.  And the most simple DNA sequence is 100's of times more complex than the first sentence of the Gettysburg Address.
    
The core challenge to evolutionary theory is to explain the chance occurrence of very long sequences of genetic symbols necessary to generate many integrated functional systems that will survive and replicate in the environment that then exists.  The challenge is formidable because the genetic sequences necessary to achieve function are extraordinarily long. Instead of spelling the first six letter word comprising the title, material causes must generate an entire novel to get life started.   
 
The core challenge to evolutionary theory is to explain the chance occurrence of very long sequences of genetic symbols necessary to generate many integrated functional systems that will survive and replicate in the environment that then exists.  The challenge is formidable because the genetic sequences necessary to achieve function are extraordinarily long. Instead of spelling the first six letter word comprising the title, material causes must generate an entire novel to get life started.   

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