a college math department consisting of 11 faculty members must choose a department head, an assistant…

a college math department consisting of 11 faculty members must choose a department head, an assistant department head, and a faculty senate representative. in how many ways can this be done?\nnumeric response

a college math department consisting of 11 faculty members must choose a department head, an assistant department head, and a faculty senate representative. in how many ways can this be done?\nnumeric response

Answer

Explanation:

Step1: Identify permutation need

We are choosing 3 distinct roles from 11 people, where order matters (each role is unique). The formula for permutations is $P(n,k)=\frac{n!}{(n-k)!}$, where $n=11$ (total faculty) and $k=3$ (positions to fill).

Step2: Calculate permutation value

$$ \begin{align*} P(11,3)&=\frac{11!}{(11-3)!}\ &=\frac{11!}{8!}\ &=11\times10\times9 \end{align*} $$

Step3: Compute final product

$11\times10\times9=990$

Answer:

990