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Combinatorics

Combinatorics is the study of permutations and combinations of groups of elements in sets. Combinatorial problems, such as magic squares, have been studied for many hundreds of years. Xenocrates (396-314 BC) is said to have determined that a total of 1 002 000 000 000 syllables could be formed from the letters of the Greek alphabet. Pascal's triangle, named after Blaise Pascal, is a useful tool for determining combinations and although it was named after Blaise Pascal (1623-1662), who discovered it in the 17th century, it was known to the Arabs in the 13th century and the Chinese in the 14th. It looks somewhat like:

           

1

           
         

1

 

1

         
       

1

 

2

 

1

       
     

1

 

3

 

3

 

1

     
   

1

 

4

 

6

 

4

 

1

   
 

1

 

5

 

10

 

10

 

5

 

1

 

1

 

6

 

15

 

20

 

15

 

6

 

1

The first and last numbers in each row are both 1, and every other number is the sum of the two above it.

Combinatorics envelops a large range of fields, including graph theory, the study of networks and probability, the study of odds of events happening.

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