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 17^{th} century, it was known to the Arabs in the 13^{th} century and the Chinese in the 14^{th}. It looks somewhat like:

1 |
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1 |
1 |
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1 |
2 |
1 |
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1 |
3 |
3 |
1 |
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1 |
4 |
6 |
4 |
1 |
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1 |
5 |
10 |
10 |
5 |
1 |
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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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