Question

How do you evaluate `""^6C_3` using Pascal's triangle?

Answer 1

`""^6C_3 = 20`

Explanation:

The `n+1`th row of Pascal's triangle consists of the binomial coefficients:

`""^nC_0, ""^nC_1, ""^nC_2, ..., ""^nC_(n-1), ""^nC_n`

So `""^6C_3` is the fourth (middle) term of the `7`th row of Pascal's triangle - the row that begins `1, 6`.

[[ Note: Some authors call the first row of Pascal's triangle the `0`th row, in which case this would be called the `6`th row ]]

So we find `""^6C_3 = 20`