TED-Ed: The mathematical secrets of Pascal's triangle - Wajdi Mohamed Ratemi

Pascal's Triangle, known by various names across cultures, is a mathematical structure filled with patterns and secrets. It is generated by starting with 1 and adding pairs of numbers to form subsequent rows. Each row corresponds to the coefficients of a binomial expansion. The triangle reveals patterns like powers of 2 and geometric shapes such as triangular and tetrahedral numbers. It also has applications in probability and combinatorics, such as calculating probabilities of family compositions or forming basketball teams. The triangle continues to intrigue mathematicians, with recent expansions into new polynomial forms.

How can Pascal's triangle be used to calculate probabilities in combinatorics?

What recent discoveries have mathematicians made regarding Pascal's triangle?