Question

Explain why the rows of Pascal’s triangle are symmetric. That is, explain why C(n, k) = C(n, (n − k))

Answer 1

The rows of Pascal’s triangle are symmetric.

Explanation:

Each row of Pascal's triangle is symmetric.

Clearly

nCr=nCn-r

since choosing r objects from n objects leaves n−r objects, and choosing n−r objects leaves r objects. This means that the coefficient of
`x^(r)` in the expansion of
`(1+x)^(n)` is the same as the coefficient of
`x^(n-r)`.