The pattern in PASCAL's triangle is a proof of mathematical interweaving

In combinatoric terms, this problem would be phrased as twelve choose five,and could be calculated with this formula,or you could just look at the sixth element of row twelve on the triangle and get your answer.The patterns in Pascal's Triangle are a testament to the elegantly interwoven fabric of mathematics.And it's still revealing fresh secrets to this day.For example, mathematicians recently discovered a way to expand it to these kinds of polynomials.What might we find next?Well, that's up to you.