In the student council elections, there are 5 candidates running for president and 5 candidates running for vice-president. How many different combinations of president and vice-president are possible?

There are 25 combinations but look at it this way. The 5 candidates for president are A, B, C, D, E then the vice president candidates are 1,2,3,4,5 see how many vice presidents A can have, then multiply by a number of presidents.

Each president can have a possibility of the 5 so ... I'm going to say 25 ...

1,1

1,2

1,3

1,4

1,5

just for president candidate number 1 there are 5 possibilities so you multiply that by 5 ...