You & a friend are at Paul & Elizabeth's Restaurant for a night of fine dining. You can choose among 2 appetizers, 4main dishes, & 3 desserts.
Appetizer: soup or salad
Main Dish: fish, chicken, beef, vegetarian
Dessert: chocolate cake, apple pie, ice cream
a: How many possible different dinners are there?
b: If there are 3 choices of salad dressing & 4 choices of ice cream, how many possible dinner combinations are there?
24
a: To calculate the number of possible different dinners, we need to multiply the number of choices for each course.
For the appetizer, there are 2 options: soup or salad.
For the main dish, there are 4 options: fish, chicken, beef, or vegetarian.
For the dessert, there are 3 options: chocolate cake, apple pie, or ice cream.
Therefore, the total number of possible different dinners is 2 (appetizer choices) x 4 (main dish choices) x 3 (dessert choices) = 24.
b: If there are 3 choices of salad dressing and 4 choices of ice cream, we can multiply the number of choices for each course again.
For the appetizer, there are 2 options: soup or salad.
For the main dish, there are 4 options: fish, chicken, beef, or vegetarian.
For the dessert, there are 3 options: chocolate cake, apple pie, or 4 choices of ice cream.
Therefore, the total number of possible dinner combinations is 2 (appetizer choices) x 4 (main dish choices) x 3 (dessert choices for cake or pie) x 4 (choices of ice cream) = 96.
a: To find the number of possible different dinners, you need to multiply the number of choices for each course.
For the appetizer, you have 2 choices (soup or salad).
For the main dish, you have 4 choices (fish, chicken, beef, or vegetarian).
For the dessert, you have 3 choices (chocolate cake, apple pie, or ice cream).
To find the total number of dinner combinations, you multiply the number of choices for each course together:
2 (appetizer choices) * 4 (main dish choices) * 3 (dessert choices) = 24 possible different dinners.
So, there are 24 possible different dinners.
b: If there are additional options for salad dressing and ice cream, you need to multiply those choices as well.
For the salad dressing, you have 3 choices.
For the ice cream, you have 4 choices.
To find the total number of dinner combinations, you multiply the number of choices for each course together:
2 (appetizer choices) * 4 (main dish choices) * 3 (dessert choices) * 3 (salad dressing choices) * 4 (ice cream choices) = 288 possible different dinners.
So, with the additional choices for salad dressing and ice cream, there are 288 possible different dinners.
a. 2*4*3=24
b. 2*4*3*3*4=288