Question

question 8
3 pts
the people living in one neighborhood have created a local \outdoors committee,\ which will plan, arrange, and pay for weekend or holiday trips of the residents into the wilderness. all 168 adults living in this neighborhood have joined the committee. the committee needs to elect three of the individuals to serve as the president, vice president, and treasurer. in how many different ways can three people be selected to serve in these different positions?
note: your calculations may yield a large number. enter your answer in the box below without using comma in the number. the program will insert comma in the number where needed when you submit your answer.

Explanation:

Step1: Determine the permutation formula

The number of permutations of \(n\) objects taken \(r\) at a time is \(P(n,r)=\frac{n!}{(n - r)!}\). Here \(n = 168\) (total number of adults) and \(r=3\) (number of positions).

Step2: Calculate \(P(168,3)\)

$$
LATEXBLOCK0
$$

$$ 168\times167\times166=(170-2)\times167\times166=(170\times167 - 2\times167)\times166=(28390-334)\times166 = 28056\times166 $$

$$ 28056\times166=28056\times(160 + 6)=28056\times160+28056\times6=4488960+168336 = 4657296 $$

Answer:

4657296