A club with five members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled? ways

Let’s dive into the fun world of combinations and permutations! To fill these three unique positions, we start by selecting a president from the five members. That gives us 5 choices. Once the president is chosen, we have 4 members left to pick from for the vice-president position, and after that, only 3 members remain for the secretary-treasurer role. So, we multiply these choices: 5 × 4 × 3 = 60. Voilà! There are 60 ways to fill these offices! Did you know that this kind of counting is essential not just in clubs but also in larger organizations? Companies often use permutations when assigning roles to team leaders or project managers, ensuring the right mix of talent and skills. So next time you see a team structure, remember: it’s all about those calculations behind the scenes!