A deli offers its cheese sandwich with various combinations of mayonnaise, lettuce, tomatoes, pickles, and sprouts. 11 types of cheese are available. How many different cheese sandwiches are possible?
Each of the ingredients are in two states, with, or without. So
number=2^5 * 12 assuming only one cheese, or no cheese is a choice
To determine the number of different cheese sandwiches, we need to calculate the total number of possible combinations of toppings and cheese.
1. Calculate the number of possible combinations for each type of topping:
- Mayonnaise: There are two possibilities, either it's included or not included.
- Lettuce: Similarly, there are two possibilities.
- Tomatoes: Two possibilities.
- Pickles: Two possibilities.
- Sprouts: Two possibilities.
2. Multiply the possibilities of each topping together to get the total number of different combinations of toppings:
2 (mayonnaise) × 2 (lettuce) × 2 (tomatoes) × 2 (pickles) × 2 (sprouts) = 2^5 = 32
3. Multiply the number of combinations of toppings by the number of cheese options available:
32 (combinations of toppings) × 11 (types of cheese) = 352
Therefore, there are 352 different cheese sandwiches possible with the given options.