(b) A company has 39 salespeople. A boardmember at the company asks for a list of the topsalespeople, ranked in order of effectiveness. How many such rankings are possible?0ExplanationCheck

Since 1 person cannot be in the top 4 salespeople more than once, then, we use combinations instead of permutations.
[tex]39C4=\frac{39!}{4!(39-4)!}[/tex]Simplify the expression,
[tex]39C4=\frac{39!}{4!35!}[/tex][tex]\begin{gathered} 39C4=\frac{39\ast38\ast37\ast36}{4\ast3\ast2\ast1} \\ 39C4=\frac{1974024}{24} \\ 39C4=82251 \end{gathered}[/tex]answer:
The 4 top list can be arranged in 82251 ways