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Mathematics

Counting, Permutations, Combinations, and the Binomial Theorem

Quick fact

The Binomial Theorem was known to mathematicians in ancient India, and in 1654 Blaise Pascal's work on the triangle (named after him) formalized the connection between combinations and binomial expansion.

Why this is interesting

You have 3 shirts and 2 pairs of pants. How many outfits can you create? That's easy—but what if you have to arrange 5 books on a shelf, or choose a committee from 20 people? The answers hide a pattern that also helps expand (x+y)^n without multiplying it out. Curious?