Note that the symboldenotes the coefficient of a^n-kb^k, or of a^kb^n-k, in the expansion of (a + b)ⁿ. Thusis the coefficient 3 of a²b or of ab² in the expansion of (a + b)³, andis the coefficient 6 of x²y² in (x + y)⁴. One readsas "binomial coefficient n choose k" or simply as "n choose k." The reason for this terminology is given in Chapter 7.

In Figure 1, we see how n and k give us the location of in the Pascal Triangle.

The number n inis the row number and k is the diagonal number if one adopts the convention of labeling the rows or diagonals as 0, 1, 2, ... .

The formulas recall the fact that the Pascal Triangle is bordered with 1's. The rule that each number inside the border of 1's in the Pascal Triangle is the sum of the two closest entries on the previous line may be written as