Curiosities · Foundation · 5 min
Pascal’s triangle
Pascal’s triangle encodes combinations through a local addition rule.
WHAT HAPPENS IF…Why is C(5,2)=10?
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To choose k objects from n, separate selections into those containing one distinguished object and those excluding it. Their counts are C(n−1,k−1) and C(n−1,k). Edge entries equal 1. Summing a row counts all subsets, giving 2ⁿ.
A detail that matters
The parity picture is a finite pattern; it does not contain infinitely many rendered details.
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