Question

(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

Answer 1

Since 1 person cannot be in the top 4 salespeople more than once, then, we use combinations instead of permutations.

`39C4=(39!)/(4!(39-4)!)`

Simplify the expression,

`39C4=(39!)/(4!35!)`
`\begin{gathered} 39C4=(39\ast38\ast37\ast36)/(4\ast3\ast2\ast1) \\ 39C4=(1974024)/(24) \\ 39C4=82251 \end{gathered}`

answer:

The 4 top list can be arranged in 82251 ways