How many ways are there to pick a five-person basketball team from 12 possible players? How many selections include the weakest and the strongest players?

Discrete Math Combination Question. How many ways are there to pick a five-person basketball team from 12 possible players? How many selections include the weakest and the strongest players?
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Step 1
If the 12 players are subdivided into 6 strongest and 6 weakest, then the number of ways to select a five person team including players from both subsets is counted by excluding the complement: we take the total count then subtract the count of ways to pick all players just from either category.
Step 2
$\left(\genfrac{}{}{0}{}{12}{5}\right)-2\phantom{\rule{thickmathspace}{0ex}}\left(\genfrac{}{}{0}{}{6}{5}\right)$