Everyone wants to watch football games on . there are 3 games on in afternoon and 3 on at night. how many different combinations of games can they watch?

Step-by-step explanation:

At afternoon there are 3 games, lets call them A1, A2, and A3. These are simultaneous, which means you can ONLY watch one of them.

At night there are other three, lets call them N1, N2 and N3. Which again, are simultaneous, so you need to chose only one.

So, you can, at most, watch 2 games: one in the afternoon (extracted from the set {A1, A2, A3}) and one at night (extracted from the set {N1, N2, N3}).

So, here what you need is ALL the possible combinations between afternoon and games. As thee choices are independent, this is, the game chosen at afternoon has no effect on the night decision, we can just multiply the number of options in every set: 3*3 = 9. So there are 9 different combinations, which are:

A1 N1, A1 N2, A1 N3, A2 N1, A2 N2, A2 N3, A3 N1, A3 N2, A3 N3.

Here I supposed you watch a game in both, night and afternoon. If you can choose to NOT watch any game, the sets will have 4 elements but the reasoning is equal.  

step-by-step explanation:

just sum

10 + 10 = 20