Q$1.$ The binomial coefficient $([n],[k])($read $"n$ choose $k")$ is defined as

$([n],[k])=\frac{n!}{(n-k)!k!}$

where the $!$ is the factorial symbol $($e$.$g$.55**4**3**2**1=120)$ and $n$ and $k$ are non$-$

negative integers with $n>k.$

$($a$)$ Write a function file that calculates $n$ choose $k$ without using Matlab's built$-$in factorial function.

This will involve multiple loops. Your function file should include if$-$statements that return an

error $($for example, disp$(\text{'}$Error$!\text{'}))$ if $n$ is less than $k$ OR if either $n$ or $k$ is negative.

$($b$)$ Using copy and paste, run your script once in the scenario where everything works, once where

$nkn$ and $an$ error message $is$ returned, and once where one $ofnorkis$ negative and $an$ error

message $is$ returned. solve with matlab