Question

How many different ways can the students at the school select the president, and the vice president, and the security from a group of 5 people?

Answer 1

P(5,3) .... or 5P3 if your textbook likes it that way ... = (5)(4)(3) = 60 ways.  

If you don't know about the permutation counting function, P(n,k) is the number of ways to pick k out of n different items, where order matters.  

P(n,k) = n(n-1)(n-2)...(n+1-k)  

It's easier to write with factorials, with P(n,k) = n!/k!, but the above is easier to compute most of the time.  

Without that, you can still solve with common sense. There are 5 ways to pick the president. For each of those, there are 4 choices left for vice president, and for each of those there are 3 choices left for secretary. 5*4*3 =  

60 total

Answer 2

15 different ways miss.