Question

Using Pascal’s triangle to generate the next row of this table.

Answer 1

The definition of the binomial coefficient is shown below

$(nBink)=\frac{n!}{k!(n-k)!}$

Notice that the top number in each 'parenthesis' corresponds to the number of row, while the number at the bottom is the column.

Therefore, the next row is

Which values are 1, 5, 10, 10, 5, 1. Those correspond to Pascal's triangle.