Apresident and a vice president for a student organization are chosen from seven people. how many different president/vice president combinations are possible?

There are 7 choices for the president, then after the president is selected, there are 6 choices left for VP. This gives 7*6 = 42 different permutations.

Order matters because of the different office titles. If we just wanted two people regardless of ordering, then we would divide by 2 to get the combination value. However, we want the permutation value in this case.

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.