To help explain, let's label these 15 different people with 15 different letters.
A B C D E F G H I J K L M N O
When the question asks how many ways can the Pres, Vice-Pres, and Secretary be chosen, it means, how many different combinations of letters (people) can we slot into those three positions. For example, I could choose "E" as Pres, "G" as Vice-Pres, and "M" as Secretary. That would be 1 way. Or, I could choose "O" as Pres, "G" as Vice-Pres, and "A" as Secretary. That would be another way.
With that in mind, we can think about how many different choices we have when selecting someone for each role. It is important to note that a single person can only have 1 role, and that they cannot be both Pres and Vice-Pres.
So, we have 15 choices for Pres. After we choose the Pres, we will only have 14 choices left for a Vice-Pres. After we choose the Vice-Pres, we will only have 13 choices left for the Secretary.
We can multiply these numbers of choices together to find the total number of possible choices that could have been made.
15 x 14 x 13 = 2730
So, there are 2730 ways to choose people for Pres, Vice-Pres, and Secretary.
Lia K.
Wow! Thank you so much for the explanation that really helped. :D05/01/21