This is Pascal's Triangle:

Pascal’s Triangle is, among other things, an array of all possible nCr’s. The outside slants equal 1, and each inside number is the sum of the two numbers diagonally above it. The first 1 in a row is the zeroth entry, then the first entry, etc. The top 1 is the zeroth row, and for every other row, the first entry in the row gives the row number. The last 1 in the nth row is always the nth entry. So: nCr = the rth entry of the nth row of Pascal’s Triangle For ex: The top 1 on Pascal’s Triangle is the zeroth row, zeroth entry, 0C0 = 1. The 3rd entry of the 6th row is 6C3 = 20.