If there are 5 teams in one league and 6 teams in another league and if each team from one league plays one team from the other league once how many games are played?

visualize the first set of teams as

a b c d e
and the second set of teams as
1 2 3 4 5 6

so we have
a1 a2 a3 a4 a5 a6
b1 b2................b6
....
e1 .....................e6

that would be 30 games

or

we have to choose one from each group
number of games = C(5,1) * C(6,1) = 5*6 = 30