compute the number of permutation that a chair, vice chair, secretary, treasurer and parliamentary can be chosen from a committee of twenty members.
20P5 = 20! / (20 - 5)!
To compute the number of permutations for choosing a chair, vice chair, secretary, treasurer, and parliamentary from a committee of twenty members, you need to use the concept of permutations.
In permutations, the order of selecting items matters. Each position in the committee can be filled by one person, and once a person is selected for a position, they cannot be selected for any other position.
The number of permutations is calculated using the formula for permutation:
P(n, r) = n! / (n - r)!
where n represents the total number of items (in this case, committee members) and r represents the number of items to be selected (in this case, committee positions).
Let's break down the calculation step by step:
1. The first position, the chair, needs to be filled by one person from twenty members. So, there are 20 choices for the chair position.
2. After selecting the chair, there are 19 remaining members. Now, for the vice chair position, there are 19 choices.
3. After selecting both the chair and vice chair, there are 18 remaining members. For the secretary position, there are 18 choices.
4. Now, we have 17 remaining members. For the treasurer position, there are 17 choices.
5. Finally, for the parliamentary position, there are 16 remaining members and 16 choices.
To calculate the total number of permutations, you multiply the number of choices at each step:
Total number of permutations = 20 * 19 * 18 * 17 * 16
Using a calculator or performing the calculation, the total number of permutations is 1,860,480.
Therefore, there are 1,860,480 different ways to select a chair, vice chair, secretary, treasurer, and parliamentary from a committee of twenty members.