There are 10 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?
See:
http://www.jiskha.com/display.cgi?id=1260057669
Note that in this problem, the positions are different, so choosing the same people for different positions is considered a different choice. There is no need to divide by 3! or n! for n positions.
a club consisting of 14 members wishes to elect a state of officers from among its membership: president, vice-president, secretary, and treasure.(no person can hold more than one office ) how many different slates are possible?
To find out how many different slates of candidates are possible, we can use the concept of permutations.
First, let's determine the number of choices for the chairperson. Since there are 10 members on the board, there are 10 candidates available for this position.
Next, let's consider the number of choices for the secretary. After the chairperson is selected, there are only 9 remaining candidates for this position, as one person has already been chosen for the chairperson role.
Finally, let's determine the number of choices for the treasurer. After the chairperson and secretary have been selected, there are 8 remaining candidates for this position.
To find the total number of possible slates of candidates, we need to multiply the number of choices for each position. Therefore, the total number of different slates of candidates is:
10 (choices for chairperson) x 9 (choices for secretary) x 8 (choices for treasurer) = 720
So, there are 720 different slates of candidates possible.