The Choose Function is defined by factorial functions as follows, $ n$/$choose $$$$$=$

Ifrac$\{$n$!\}\{$k$!($n$-$k$)!\}$$$,$ when $k1,$ or $1$ when $k=0.$

a$)$ Write a factorial function using a for loop to calculate $n!$ where the function take $n$

as an argument. $($See page $76$ for an example.$)$

b$)$ Check that your factorial function works with $n=4,5$ and $6.$

c$)$ Write a choose function that takes $n$ and $k$ as arguments. This function should

use multiple calls to your factorial function to calculate the Choose Function.

d$)$ Upgrade your factorial fuction using the recursion method in Exercise $2\mathrm{.}13.$ Make

sure to give it a different name than your factorial function from part a$).$