3.38: Forming 5-digit numbers and mixed teams

A $5$-digit number is to be formed using $5$ different digits from $1$–$9$. No digit may be used more than once.

Find how many $5$-digit numbers can be formed.

Find how many of these $5$-digit numbers are greater than $50\,000$ and even.

A team of $9$ is chosen from $6$ doctors, $4$ dentists and $2$ nurses. Find how many teams include at least $2$ doctors, at least $2$ dentists and at least $2$ nurses.