Page 3: About Pascal’s Triangle

Unit 8, Lab 5, Page 3

In Pascal’s Triangle, each number is 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 rowitems. So, if you want to choose 2 people from 6 (say, Alphie, Betsy, Gamal, Delia, Eva, and Frank), there are 15 (row 6, column 2) ways to do it:

  1. Alphie and Betsy

  2. Alphie and Gamal

  3. Alphie and Delia

  4. Alphie and Eva

  5. Alphie and Frank

  6. Betsy and Gamal

  7. Betsy and Delia

  8. Betsy and Eva

  9. Betsy and Frank

  10. Gamal and Delia

  11. Gamal and Eva

  12. Gamal and Frank

  13. Delia and Eva

  14. Delia and Frank

  15. Eva and Frank