Combinations (Make sets, combining only a few options)
Find the number of possible combinations, with the given conditions:
| Meats | Vegetables | Cheese |
| Pepperoni | Peppers | Mozzerella |
| Sausage | Mushrooms | Ricotta |
| Meatballs | Tomatos | |
| Onions |
1. You are ordering a pizza off of the menu above. If you can choose up to 1 meat, up to 2 vegetables, and must have 1 cheese, how many pizzas can you make?
| No meat options | Pepperoni | Sausage | Meatballs |
| peppers & mushrooms | peppers & mushrooms | peppers & mushrooms | peppers & mushrooms |
| peppers & tomatos | peppers & tomatos | peppers & tomatos | peppers & tomatos |
| peppers & onions | peppers & onions | peppers & onions | peppers & onions |
| mushrooms & tomatos | mushrooms & tomatos | mushrooms & tomatos | mushrooms & tomatos |
| mushrooms & onions | mushrooms & onions | mushrooms & onions | mushrooms & onions |
| tomatos & onions | tomatos & onions | tomatos & onions | tomatos & onions |
| peppers only | peppers only | peppers only | peppers only |
| mushrooms only | mushrooms only | mushrooms only | mushrooms only |
| tomatos only | tomatos only | tomatos only | tomatos only |
| onions only | onions only | onions only | onions only |
| no vegetables | no vegetables | no vegetables | no vegetables |
| x2 (for mozzerella or ricotta) | x2 (for mozzerella or ricotta) | x2 (for mozzerella or ricotta) | x2 (for mozzerella or ricotta) |
4 meat options x 11 veggie options x 2 cheese options = 88 pizzas
2. If, given the same options, you can choose up to 2 meats, up to 2 vegetables, and must have 1 cheese, how many pizzas can you make?
| No meat options | Pepperoni only | Sausage only | Meatballs only |
| peppers & mushrooms | peppers & mushrooms | peppers & mushrooms | peppers & mushrooms |
| peppers & tomatos | peppers & tomatos | peppers & tomatos | peppers & tomatos |
| peppers & onions | peppers & onions | peppers & onions | peppers & onions |
| mushrooms & tomatos | mushrooms & tomatos | mushrooms & tomatos | mushrooms & tomatos |
| mushrooms & onions | mushrooms & onions | mushrooms & onions | mushrooms & onions |
| tomatos & onions | tomatos & onions | tomatos & onions | tomatos & onions |
| peppers only | peppers only | peppers only | peppers only |
| mushrooms only | mushrooms only | mushrooms only | mushrooms only |
| tomatos only | tomatos only | tomatos only | tomatos only |
| onions only | onions only | onions only | onions only |
| no vegetables | no vegetables | no vegetables | no vegetables |
| x2 (for mozzerella or ricotta) | x2 (for mozzerella or ricotta) | x2 (for mozzerella or ricotta) | x2 (for mozzerella or ricotta) |
| Pepperoni & sausage | Pepperoni & meatballs | Sausage & meatballs |
| peppers & mushrooms | peppers & mushrooms | peppers & mushrooms |
| peppers & tomatos | peppers & tomatos | peppers & tomatos |
| peppers & onions | peppers & onions | peppers & onions |
| mushrooms & tomatos | mushrooms & tomatos | mushrooms & tomatos |
| mushrooms & onions | mushrooms & onions | mushrooms & onions |
| tomatos & onions | tomatos & onions | tomatos & onions |
| peppers only | peppers only | peppers only |
| mushrooms only | mushrooms only | mushrooms only |
| tomatos only | tomatos only | tomatos only |
| onions only | onions only | onions only |
| no vegetables | no vegetables | no vegetables |
| x2 (for mozzerella or ricotta) | x2 (for mozzerella or ricotta) | x2 (for mozzerella or ricotta) |
7 meat options x 11 veggie options x 2 cheese options = 154 pizzas
3. If, given the same options, you may choose up to just one meat OR vegetable, and must choose 1 cheese, how many pizzas can you make?
| Mozzerella | Ricotta |
| peppers | peppers |
| mushrooms | mushrooms |
| onions | onions |
| tomatos | tomatos |
| pepperoni | pepperoni |
| sausage | sausage |
| meatball | meatball |
| no meat or vegetable | no meat or vegetable |
2 cheese options x 8 meat/vegetable options= 16 pizzas
| Shirts | Pants | Shorts |
| Green T | Cargo pants | Khaki shorts |
| Black T | Dress pants | Swim shorts |
| Button Down | Leggings | |
| Sweat pants |
4. You are packing for a weekend trip. How many sets of clothing can you back if you must bring 2 shirts, two pants, and two shorts?
| Green T & Black T | Green T & Button Down | Black T & Button Down |
| cargo pants & dress pants | cargo pants & dress pants | cargo pants & dress pants |
| cargo pants & leggings | cargo pants & leggings | cargo pants & leggings |
| cargo pants & sweat pants | cargo pants & sweat pants | cargo pants & sweat pants |
| dress pants & leggings | dress pants & leggings | dress pants & leggings |
| dress pants & sweat pants | dress pants & sweat pants | dress pants & sweat pants |
| leggings & sweat pants | leggings & sweat pants | leggings & sweat pants |
| (must bring both shorts) | (must bring both shorts) | (must bring both shorts) |
3 shirt options x 6 pants options x 1 shorts option = 18 packing combinations.
5. If, given the same options, you can choose up to 2 shirts, up to 3 pants, and up to 2 shorts, how many packing combinations do you have?
| Green T & Black T | Green T & Button Down | Black T & Button Down |
| cargo pants & dress pants & leggings | cargo pants & dress pants & leggings | cargo pants & dress pants & leggings |
| cargo pants & dress pants & sweat pants | cargo pants & dress pants & sweat pants | cargo pants & dress pants & sweat pants |
| cargo pants & leggings & sweat pants | cargo pants & leggings & sweat pants | cargo pants & leggings & sweat pants |
| dress pants & leggings & sweat pants | dress pants & leggings & sweat pants | dress pants & leggings & sweat pants |
| cargo pants & dress pants | cargo pants & dress pants | cargo pants & dress pants |
| cargo pants & leggings | cargo pants & leggings | cargo pants & leggings |
| cargo pants & sweat pants | cargo pants & sweat pants | cargo pants & sweat pants |
| dress pants & leggings | dress pants & leggings | dress pants & leggings |
| dress pants & sweat pants | dress pants & sweat pants | dress pants & sweat pants |
| leggings & sweat pants | leggings & sweat pants | leggings & sweat pants |
| cargo pants | cargo pants | cargo pants |
| dress pants | dress pants | dress pants |
| leggings | leggings | leggings |
| sweat pants | sweat pants | sweat pants |
| no pants | no pants | no pants |
| x khaki shorts & swim shorts | x khaki shorts & swim shorts | x khaki shorts & swim shorts |
| x khaki shorts only | x khaki shorts only | x khaki shorts only |
| x swim shorts only | x swim shorts only | x swim shorts only |
| x no shorts | x no shorts | x no shorts |
| Green T only | Black T only | Button Down only | No shirt |
| cargo pants & dress pants & leggings | cargo pants & dress pants & leggings | cargo pants & dress pants & leggings | cargo pants & dress pants & leggings |
| cargo pants & dress pants & sweat pants | cargo pants & dress pants & sweat pants | cargo pants & dress pants & sweat pants | cargo pants & dress pants & sweat pants |
| cargo pants & leggings & sweat pants | cargo pants & leggings & sweat pants | cargo pants & leggings & sweat pants | cargo pants & leggings & sweat pants |
| dress pants & leggings & sweat pants | dress pants & leggings & sweat pants | dress pants & leggings & sweat pants | dress pants & leggings & sweat pants |
| cargo pants & dress pants | cargo pants & dress pants | cargo pants & dress pants | cargo pants & dress pants |
| cargo pants & leggings | cargo pants & leggings | cargo pants & leggings | cargo pants & leggings |
| cargo pants & sweat pants | cargo pants & sweat pants | cargo pants & sweat pants | cargo pants & sweat pants |
| dress pants & leggings | dress pants & leggings | dress pants & leggings | dress pants & leggings |
| dress pants & sweat pants | dress pants & sweat pants | dress pants & sweat pants | dress pants & sweat pants |
| leggings & sweat pants | leggings & sweat pants | leggings & sweat pants | leggings & sweat pants |
| cargo pants | cargo pants | cargo pants | cargo pants |
| dress pants | dress pants | dress pants | dress pants |
| leggings | leggings | leggings | leggings |
| sweat pants | sweat pants | sweat pants | sweat pants |
| no pants | no pants | no pants | no pants |
| x khaki shorts & swim shorts | x khaki shorts & swim shorts | x khaki shorts & swim shorts | x khaki shorts & swim shorts |
| x khaki shorts only | x khaki shorts only | x khaki shorts only | x khaki shorts only |
| x swim shorts only | x swim shorts only | x swim shorts only | x swim shorts only |
| x no shorts | x no shorts | x no shorts | x no shorts |
7 shirt options x 15 pants options x 4 shorts options = 420 packing combinations
6. If, given the same options, will choose up to 2 shirts and must choose 2 pants OR shorts, how many packing combination will you have?
| Green T only | Black T only | Button Down only | No shirt |
| cargo pants & dress pants | cargo pants & dress pants | cargo pants & dress pants | cargo pants & dress pants |
| cargo pants & leggings | cargo pants & leggings | cargo pants & leggings | cargo pants & leggings |
| cargo pants & sweat pants | cargo pants & sweat pants | cargo pants & sweat pants | cargo pants & sweat pants |
| cargo pants & khaki shorts | cargo pants & khaki shorts | cargo pants & khaki shorts | cargo pants & khaki shorts |
| cargo pants & swim shorts | cargo pants & swim shorts | cargo pants & swim shorts | cargo pants & swim shorts |
| dress pants & leggings | dress pants & leggings | dress pants & leggings | dress pants & leggings |
| dress pants & sweat pants | dress pants & sweat pants | dress pants & sweat pants | dress pants & sweat pants |
| dress pants & khaki shorts | dress pants & khaki shorts | dress pants & khaki shorts | dress pants & khaki shorts |
| dress pants & swim shorts | dress pants & swim shorts | dress pants & swim shorts | dress pants & swim shorts |
| leggings & sweat pants | leggings & sweat pants | leggings & sweat pants | leggings & sweat pants |
| leggings & khaki shorts | leggings & khaki shorts | leggings & khaki shorts | leggings & khaki shorts |
| leggings & swim shorts | leggings & swim shorts | leggings & swim shorts | leggings & swim shorts |
| sweat pants & khaki shorts | sweat pants & khaki shorts | sweat pants & khaki shorts | sweat pants & khaki shorts |
| sweat pants & swim shorts | sweat pants & swim shorts | sweat pants & swim shorts | sweat pants & swim shorts |
| khaki shorts & swim shorts | khaki shorts & swim shorts | khaki shorts & swim shorts | khaki shorts & swim shorts |
| Green T & Black T | Green T & Button Down | Black T & Button Down |
| cargo pants & dress pants | cargo pants & dress pants | cargo pants & dress pants |
| cargo pants & leggings | cargo pants & leggings | cargo pants & leggings |
| cargo pants & sweat pants | cargo pants & sweat pants | cargo pants & sweat pants |
| cargo pants & khaki shorts | cargo pants & khaki shorts | cargo pants & khaki shorts |
| cargo pants & swim shorts | cargo pants & swim shorts | cargo pants & swim shorts |
| dress pants & leggings | dress pants & leggings | dress pants & leggings |
| dress pants & sweat pants | dress pants & sweat pants | dress pants & sweat pants |
| dress pants & khaki shorts | dress pants & khaki shorts | dress pants & khaki shorts |
| dress pants & swim shorts | dress pants & swim shorts | dress pants & swim shorts |
| leggings & sweat pants | leggings & sweat pants | leggings & sweat pants |
| leggings & khaki shorts | leggings & khaki shorts | leggings & khaki shorts |
| leggings & swim shorts | leggings & swim shorts | leggings & swim shorts |
| sweat pants & khaki shorts | sweat pants & khaki shorts | sweat pants & khaki shorts |
| sweat pants & swim shorts | sweat pants & swim shorts | sweat pants & swim shorts |
| khaki shorts & swim shorts | khaki shorts & swim shorts | khaki shorts & swim shorts |
7 shirt options x 15 pants/shorts options = 105 packing combinations