Chapter 9.1, Problem 12E

Solution

To calculate: The numbers of lists consisting 6 projects that can be made from a list of 12 projects based on priority so that the mayor will send the list to the city council for funding.

The resultant answer is $665,280$ lists.

Given information:

Among 12 projects, lists of 6 projects have to be made based on priority so that the mayor will send the list to the city council for funding.

Formula used: The number of permutations of n objects taken r at a time denoted by $P_{n_r}$ and given by $P_{n_r}=\frac{n!}{\left(n-r\right)!}$ .

Calculation:

Total number of project is 12. Out of it lists of 6 projects have to be made.

The expression can be written as,

  $P_{{12}_6}$

Rewrite the expression using the formula $P_{n_r}=\frac{n!}{\left(n-r\right)!}$ ,

  $\begin{array}{c}{P}_{{12}_6}=\frac{12!}{\left(12-6\right)!}\\ =\frac{12!}{6!}\end{array}$

Now expand the factorial,

  $\frac{12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6!}{6!}=665,280$

Therefore, the value of $P_{{12}_6}$ is $665,280$ . It means $665,280$ lists of 6 projects can be made.