Problem $3.$

$(15$ points$)$

For this problem, you can use the exclamation mark for factorials. If you want to enter $(n{)}_r,$ you must type: $\frac{n!}{n-r}!.$

A company has three $($distinct$)$ positions available: a Java programmer, a PHP prognammer, and a repair technician.

There are $63$ applicants from $3$ schools, A$,$ B$,$ and C$,$ with $8$ applicants from A$,18$ applicants from B$,$ and $37$ applicants from C$.$

The company must hire three different people $($no repeats$).$

How many ways can the hiring be done...

$($a$)$ if the company picks three people from the entire pool of $63$ applicants $($in other words there are no other restrictions$)?$

$($b$)$ if the Java programmer is from school A$,$ the PHP programmer is from school B$,$ and the repair technician is from school C$?$

##:

:

$($d$)$ if the company hires the Java programmer from school A first, and then afterwards picks two people from the remaining $62$ applicants?

$($e$)$ if neither $($none$)$ of the programmers are from school $C($no restrictions on the technician$)?$