c. ricardo is one of the sales people. he determined that there are _{17}c_{7} number of ways to line up the…

Explanation:

Step1: Analyze Ricardo's error

Ricardo used a combination formula ({n}C{r}=\frac{n!}{r!(n - r)!}) which is for choosing (r) elements from (n) elements without considering order. But lining - up people is a permutation problem (order matters).

Step2: Calculate the correct number of ways for lining - up

If there are (n) people in the sales department, the number of ways to line them up is (n!). Let's assume there are (n) people in the sales department. The correct number of ways to line them up for a picture is (n!) (where (n) is the number of sales people).

Step3: Solve part d

Since Ricardo must be on the committee, we need to choose (4) more sales people out of the remaining sales people (say there are (s) total sales people, so we choose (4) from (s - 1)). The number of ways to choose (4) sales people out of (s - 1) is ({s - 1}C{4}=\frac{(s - 1)!}{4!(s - 1-4)!}). The number of ways to choose (2) customer - service reps (say there are (c) customer - service reps) is ({c}C{2}=\frac{c!}{2!(c - 2)!}), and the number of ways to choose (1) human - resource rep (say there are (h) human - resource reps) is ({h}C{1}=\frac{h!}{1!(h - 1)!}=h). The total number of possible committees is ({s - 1}C{4}\times_{c}C_{2}\times h=\frac{(s - 1)!}{4!(s - 5)!}\times\frac{c!}{2!(c - 2)!}\times h)

Answer:

For part c: The error is using combination instead of permutation. The correct number of ways to line up is (n!) (where (n) is the number of sales people). For part d: (\frac{(s - 1)!}{4!(s - 5)!}\times\frac{c!}{2!(c - 2)!}\times h) (where (s) is the total number of sales people, (c) is the total number of customer - service reps, and (h) is the total number of human - resource reps)