A company is issuing new employee IDs consisting of $2$ letters from the English alphabet, followed by a $3-$digit number.

$($a$)(3$ points$)$ How many employee IDs can be made under these conditions?

$($b$)(4$ points$)$ A new policy is being instituted at the company. Each ID now must satisfy the following guidelines:

The two chosen letters must now be distinct from one another

Since the number $\text{'}0\text{'}$ is similar to the letter $\text{'}O\text{'},$ neither are allowed to be used

The $3-$digit number must now be smaller than $500$

Under these guidelines, how many IDs can be created?

Stagel: $25,25\mathrm{.}24\mathrm{.}4\mathrm{.}9\mathrm{.}9$

$2$:$24,194,400$

$3$:$4,194$

$4$:$9,$

$5$:$9,$

$($c$)(3$ points$)$ Oh no$!$ The company is running out of IDs to assign to new employees. Suggest a way to increse the number of IDs that can be produced while still following the guidelines in the previous part.