A triangle of numbers in which the rth item on the nth row is the value of n−1Cr−1, the number of different combinations of (r−1) objects chosen from (n−1). The sum of the numbers on the nth row is 2n−1. Thus 6−1C4−1=5C3=10. Apart from the 1 at the beginning and end of each row, each number is the sum of the two nearest numbers in the row above. For example 10=4+6.
The relevance of the numbers in the context of probability was noted by Pascal and the description ‘Pascal's triangle’ was first used in a book on probability by Montmort.
Subjects: Probability and Statistics.