Definition The binomial coefficient

$($n

k

$)$

$($read $$n choose k$)$ is defined as

$($n

k

$)$

$=$ n$!$

$($n $$ k$)!$ k$!$

where the $!$ is the factorial symbol $($e$.$g$.5!=5*4*3*2*1=120)$ and n and k are non$-$negative

integers with n $>$ k$.$

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

This will involve multiple loops.

$-$ Your script should include if$-$statements that return an error $($for example, disp$($Danger

Will Robinson!$))$ if n is less than k OR if either n or k is negative.

$($b$)$ Divide your script into three sections using the command $\%\%.$ Copy and paste your script into each

section and run the scripts $($i$)$ once in the scenario where everything works, $($ii$)$ once where n $<$ k

and an error message is returned, and $($iii$)$ once where one of n or k is negative and an error message

is returned.