A 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)
4 choices of appetizers,
6 choose 2 entrees= (6,2) = 6*5/2 = 15
3 choices of desserts.
Multiply the choices together to get the total number of different dinners.
To find out how many different dinner combinations can be selected, we need to multiply the number of choices for each course.
First, let's determine the number of choices for each course:
1. Appetizers: There are 4 appetizers to choose from, and since dinners share one appetizer, each dinner has 4 choices.
2. Entrees: Each dinner can choose 2 entrees out of the 6 available. To select 2 entrees without repetition, we can use the combination formula. The number of combinations of k things taken from n things without repetition is given by nCk, which is calculated as n! / (k! * (n-k)!). In this case, we have n = 6 (number of entrees) and k = 2 (number of entrees to be chosen). Therefore, the number of choices for entrees is 6C2 = 6! / (2! * (6-2)!) = 15.
3. Desserts: Just like the appetizers, dinners share one dessert, and there are 3 desserts to choose from. So, each dinner has 3 choices for dessert.
Now, we can multiply the number of choices for each course to find the total number of dinner combinations:
Total number of dinner combinations = Number of choices for appetizers * Number of choices for entrees * Number of choices for desserts
Total number of dinner combinations = 4 * 15 * 3
Total number of dinner combinations = 180
Therefore, there are 180 different dinner combinations that can be selected.