Acerca del Triángulo de Pascal

In Pascal's Triangle, each number in the sum of the two numbers above it, with ones on the outside:

Row 1:    1  1
Row 2:    1  2  1
Row 3:    1  3  3  1
Row 4:    1  4  6  4  1
Row 5:    1  5  10  10  5  1
Row 6:    1  6  15  20  15  6  1
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Pascal's Triangle is named (among Europeans and their cultural descendents) after the mathematician Blaise Pascal, who published a detailed study of the triangle in 1653, although the earliest surviving reference to the triangle comes from the Hindu mathematician Pingala, who lived some time around the 4th to 2nd century BCE.

Within a row of Pascal's Triangle, count columns from zero, not one. Row 6, Column 2 is 15. The phrase 6 choose 2 refers to this number.
Numbers in Pascal's Triangle tell you how many ways you can choose column items from a set of row items. So, if you want to choose 2 people from 6 (say, Morgan, Jasmine, Omar, Delia, Eva, and Frank), there are 15 (row 6, column 2) ways to do it:
  1. Morgan and Jasmine
  2. Morgan and Omar
  3. Morgan and Delia
  4. Morgan and Eva
  5. Morgan and Frank
  6. Jasmine and Omar
  7. Jasmine and Delia
  8. Jasmine and Eva
  9. Jasmine and Frank
  10. Omar and Delia
  11. Omar and Eva
  12. Omar and Frank
  13. Delia and Eva
  14. Delia and Frank
  15. Eva and Frank