Remember C stands for "Collecting" and P stands for "Positioning".

Also C stands for "Combinations" and P stands for "Permutations".

So ask this question:

Q:  After selecting the 5 people, are we only COLLECTING them, or are we 
POSITIONING them?

A:  Since "president, vice president, secretary, treasurer, and historian"
are POSITIONS, we are POSITIONING them.  So we use permutations.

So the notation is:

30 members, POSITION 5 

and the notation is 

30P5 or P(30,5) or 30P5 or ,
depending on which notation your teacher uses.  

Formula:  Start with 30 and use 5 factors, each factor 1 less than 
the previous one:

Solution:  30×29×28×27×26 = 17100720

Edwin