1782582251jalbert4250

Here’s the data:

For a video game, there are 6 heroes, but you can only take 4 into battle.

Each hero can have 1 pet assigned to them, or no pet. The pets can be assigned to any hero. There are 12 different pets.

Each hero also has 8 different pieces of equipment (for this example) that you can equip to them that is specific to that hero, but you must equip 2 and only 2.

How many combinations are there of 4 heroes, each with 1 pet and 2 pieces of equipment?

How do you calculate the total combinations and then account for only being able to use 4 of the 6 heroes?

How many possible combinations of the in-game screen are there? How many different possible combinations are available to the player to take into battle?

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What I got so far, not sure,

7+6+5+4+3+2+1= 28 combinations of equipment per hero. Each with 1 of 12 pets. So for the first slot, there are 28×12=336 different possibilities. Then for the second slot, there are 11 pets to choose from = 308. Then 10 for slot 3=280, and 252 for slot 4, 336+308+280+252=1176.

At first that makes sense but don’t you have to account for all possible options in the slot? Obviously, It doesn’t matter the order of the heroes, but for example the first slot there are 336 possibilities per hero with 6 heroes to choose from 336×6=2016, then for the second slot there’s only 5 heroes to choose from, etc? So 2016+(308×5)+(280×4)+(252×3)=5,432

Are either of these right? It seems like the second one is right or at least closer because it accounts for adding more heroes to the game, which should increase the number of combinations, even if you can only pick 4. I think I’m just overthinking it lol.

I just realized that you can also not have a pet assigned and that option is available for all 4 heroes. So technically you could have 3 heroes without a pet and 12 options for the 4th hero.

Thank you if you know and care to explain!