A local civic club has 20 members. to reorganize their leadership they will need to select a new president, vice-president, and secretary. how many ways can this be done if these leadership positions can be filled by any of the club members?

Basically, the question is asking how many ways 20 people can occupy 3 positions. We'll use combination Combination is a method of selection of items from a collection, such that the order of selection does not matter. So we have 20C3 ways where C denotes combination. C (20,3) = 20! / (3! (20â’3) !) = (20 * 19 * 18 * 17 * ... 3 * 2 * 1) / (3 * 2 * 1 * (17!)) 17! = 17 * 16 * ... * 2 * 1 So C (20,3) = 20! / (3! (20â’3) !) = 1140