To determine the number of ways the three offices can be filled, we can consider the following:
For the president position, we have 15 choices since any of the 15 members can be selected.
For the vice-president position, once the president is chosen, we have 14 remaining members to choose from.
For the secretary-treasurer position, after the president and vice-president have been chosen, we have 13 remaining members to choose from.
To calculate the total number of ways the three offices can be filled, we can multiply the number of choices for each position:
Number of ways = 15 (choices for president) × 14 (choices for vice-president) × 13 (choices for secretary-treasurer)
Number of ways = 2,730
Answers , there are 2,730 ways the three offices can be filled with the given conditions.
