restaurant offers a $20 dinner deal. Dinners share one of 4 appetizers, get 2 of 6 entrees and share one of 3 desserts. How many dinners can be selected? (To make it easier, let’s assume they don’t pick 2 of the same meal)
http://www.jiskha.com/display.cgi?id=1310328720
To find the number of different dinners that can be selected, we need to determine the number of choices for each part of the meal.
1. Appetizers: There are 4 different appetizers to choose from, and all dinners share one appetizer. So, there is only 1 choice for the appetizer.
Number of choices for appetizers = 1
2. Entrees: Each dinner gets to choose 2 out of 6 entrees. Since they cannot pick two of the same meal, we need to calculate the number of combinations of choosing 2 entrees out of 6 without repetitions. This can be calculated using the formula for combinations: nCr = n! / (r! * (n - r)!), where n is the total number of options and r is the number of choices.
Number of choices for entrees = 6C2 = 6! / (2! * (6-2)!) = (6 * 5) / (2 * 1) = 15
3. Desserts: All dinners share one dessert, so there is only 1 choice for the dessert.
Number of choices for desserts = 1
To find the total number of dinner combinations, we multiply the number of choices for each part:
Total number of dinner combinations = Number of choices for appetizers * Number of choices for entrees * Number of choices for desserts
= 1 * 15 * 1
= 15
Therefore, there are 15 different dinners that can be selected.