Ryan B. answered • 09/30/20
MBA working in Finance
There are two possible interpretations of this questions.
The first one would be: how many distinct groups of three members can hold the club offices? In this interpretation, if members 1, 2, and 3 hold all the cabinet positions, it doesn’t matter which ones they hold.
This interpretation would be a combination. The formula for a combination is n!/((n-r)r!), where n is the number of members and r is the number of positions. Thus, the number of combinations would be 16!/((16-3)!*3!) = 560/
The second interpretation: the position each member holds is important. If members 1, 2, and 3 hold all of the cabinet positions, every arrangement of those three members among the positions is a unique outcome.
This interpretation would be a permutation. The formula for a permutation is n!/(n-r)!. N and R represent the same variables as they do in the combination example above. Thus, the number of permutations would be 16!/(16-3)! = 3,360
