A club elects a president, vice -president, and secretary-treasurer. How many sets of officers are possible if there are 15 members and any member can be elected to each position? No person can hold more than one office.
15P3 = 15*14*13
To find the number of possible sets of officers, we need to multiply the number of choices for each position.
We know that the president has 15 choices, as any member can be elected to this position. After the president is elected, there are 14 members remaining who can be chosen for the vice-president position.
Once the vice-president is elected, there are 13 members left who can be selected for the secretary-treasurer position.
To find the total number of possible sets of officers, we can multiply the number of choices for each position:
Total number of sets of officers = Number of choices for president × Number of choices for vice-president × Number of choices for secretary-treasurer
Total number of sets of officers = 15 × 14 × 13
Total number of sets of officers = 2,730
Therefore, there are 2,730 possible sets of officers for the club.