1.22 Pascal’s triangle

$$1$$

$$1\quad 1$$

$$1\quad 2\quad 1$$

$$1\quad 3\quad 3\quad 1$$

$$1\quad 4\quad 6\quad 4\quad 1$$

$$1\quad 5\quad 10\quad 10\quad 5\quad 1$$

$$1\quad 6\quad 15\quad 20\quad 15\quad 6\quad 1$$

In this case, the binomial coefficients are given by Pascal’s triangle, and are pronounced ‘$n\,$ choose $k\,$’. If we list the rows by $n=0,1,2,\dots$ from the top, and the entries in each row from the left by $k=0,1,\dots,n$, then ${{n}\choose{0}}=1$,