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![A small college with 1,200 total students has a student government of 40 members. From its members, the student government will elect a president, vice president, secretary, and treasurer. No single member can hold more than 1 of these 4 positions.
The permutation formula
nPr can be used to find the number of unique ways the student government can arrange its members into these positions.
What are the appropriate values of
n and
r ?
{:[n=◻],[r=◻]:}](https://externalquestionsimg-a4fuc2b6e0gtdqge.z01.azurefd.net/external-question-images/images/images/ka/PreCalculus/Probability%20and%20combinatorics/Permutations/Q-10.png)
A small college with , total students has a student government of members. From its members, the student government will elect a president, vice president, secretary, and treasurer. No single member can hold more than of these positions.The permutation formula can be used to find the number of unique ways the student government can arrange its members into these positions.What are the appropriate values of and ?
Full solution
Q. A small college with , total students has a student government of members. From its members, the student government will elect a president, vice president, secretary, and treasurer. No single member can hold more than of these positions.The permutation formula can be used to find the number of unique ways the student government can arrange its members into these positions.What are the appropriate values of and ?
- Determine and : We need to determine the values of and for the permutation formula , which is used to calculate the number of ways to arrange objects from a set of distinct objects, where the order matters and repetitions are not allowed. In this context, represents the total number of student government members available for the positions, and represents the number of positions to be filled.
- Identify values: Since the student government has members and we are looking to fill distinct positions (president, vice president, secretary, and treasurer), the value of is the total number of members, which is .
- Calculate and : The value of is the number of positions to be filled, which is , as no member can hold more than one of these positions simultaneously.
- Use permutation formula: Now that we have the values of and , we can use them in the permutation formula. However, since the question only asks for the values of and , we do not need to perform the actual permutation calculation.
