the arcade has three pinball machines and five video games.

Question

the arcade has three pinball machines and five video games. if a person wants to play one pinball machine and one video game, how many different combinations of games could that person play?

Answer 1

Consider playing pinball first and video second.  There are 3 possible choices for the first game and 5 possible choices for the second game, hence 15 possible ways of playing the games in that sequence.  We do not consider the reverse sequence because it is the combinations of games that is requested.