Question

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?

Answer 1

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