Question

you recently joined a computer club that now has 14 members. the club has four different leadership positions (president, vice president, treasurer and secretary). if any club member can serve in any of the leadership positions but no one can serve in two positions simultaneously, how many different ways can the club leadership be organized?

Answer 1

There are 14 members in the club, and there are 4 leadership positions. Each position can be filled by any of the 14 members, so there are 14 ways to fill the first position, 14 ways to fill the second position, and so on. However, we have overcounted because we have not taken into account that a member cannot serve in two positions simultaneously. To correct for this overcounting, we divide by the number of ways that a member can serve in two positions simultaneously, which is 1. Therefore, the total number of ways that the club leadership can be organized is:

14 * 14 * 14 * 14 / 1 = 14^4 = 20736 ways.