Discrete Math: 03. Combinatorial Proof on Pascal's Triangle
There is a straightforward way to build Pascal's Triangle by defining the value of a term to be the the sum of the adjacent two entries in the row above it. We also know that Pascal's Triangle contains the binomial coefficients nCk. In this video I provide a combinatorial proof to show why this technique for building Pascal's Triangle works with the numbers nCk. The technique I use is a method called "counting in two ways", which is a very useful proof technique in discrete mathematics.
An introduction to Discrete Math by Dr. Sarada Herke.
Links to the related videos:
• Discrete Math: 01. Binomial Coefficients i... - Discrete Math: 01. Binomial Coefficients in Pascal's Triangle
• Discrete Math: 02. Rowsums of Pascal's Tri... - Discrete Math: 02. Rowsums of Pascal's Triangle
• Mathsplanations: 5 Reasons to like Pascal'... - 5 Reasons to like Pascal's Triangle
• Math Skills: How to find Factorial, Permut... - Math Skills: How to find Factorial, Permutation and Combination (Choose)
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"Spoonful of Maths" - / spoonfulofmaths