In how many ways may the position of president and vice president be given to six nominees?

We have 6 nominees, let's call them a,b,c,d,e,f, and two positions President and Vice President. Let's say one variation is a is President and b is Vice President which we will call (a,b). Now, we may list out all possibilities of a as President: (a,b), (a,c), (a,d), (a,e) and (a,f). There are 5 in total, but since we have 6 candidates, the total possibilities are 6x5 = 30. This is a case of permutations, not combinations, because (a,b) is different from (b,a). The equation for permutations is n!/(n-r)! = 6!/(6-2)!= 6*5 = 30.