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

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Answer 1 · 2018-02-28T00:37:51

$""^6C_3 = 20$

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 ]]

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

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