Some weekend combinatorics

Combinatorics problems (each one builds on the previous one):

  • If there’s a sequence of tasks you need to do, and you know how many ways there are to do each task, how many ways are there to do the whole sequence?
  • How many ways are there to rearrange the letters of a word?
  • Pick a spot on a grid. How many ways are there to go from the top-left to the spot using only steps to the right and steps down?
  • This leads to Pascal’s triangle, which has all sorts of patterns.
  • Here’s a weird one of those patterns: if you raise 11 to some power n, the answer will match the nth row of Pascal’s triangle! Why is this?

Simon got this from James Tanton’s course on Permutations and Combinations on

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