A student club with 30 members need to chose officers. There are five officer positions and no member can occupy two positions at the same time. How many poss

Question

 A student club with 30 members need to chose officers. There are five officer positions and no member can occupy two positions at the same time. How many possible slates of candidates are there? 

 

30!/(5!25!)


25!/30!


30!/5!


30!

Answer 1

The problem doesn't make this totally clear, but I'm going to assume that the different officer positions are unique -- that is, order will matter when assigning members to the positions. For this type of system, where order matters and you cannot repeat entries, the formula is

 

n! / (n - k)!

 

where n = 30 is the number of members and k = 5 is the number of "slots" (on https://www.mathsisfun.com/combinatorics/combinations-permutations.html, this is called a permutation without repetition). Thus, the answer is 

 

30! / 5!