Question

brett is planning a banquet for 125 guests. he needs to select 4 appetizers, 4 entrees, and 2 side dishes. carson's catering has 18 appetizers, 12 entrees, and 14 side dishes to choose from. how many different ways are there for brett to plan the menu?

Answer 1

To calculate the number of different ways Brett can plan the menu, we need to multiply the number of choices for each category: appetizers, entrees, and side dishes. Using the formula nCr = n! / (r! * (n-r)!), we can calculate each combination separately and then multiply them to find the total number of ways.

Step-by-step explanation:

To calculate the number of different ways Brett can plan the menu, we need to multiply the number of choices for each category. Brett needs to select 4 appetizers out of 18 choices, which can be represented as 18C4. Similarly, he needs to select 4 entrees out of 12 choices, which can be represented as 12C4. Finally, he needs to select 2 side dishes out of 14 choices, which can be represented as 14C2.

To find the total number of ways, we need to multiply these combinations together: 18C4 * 12C4 * 14C2. Using the formula nCr = n! / (r! * (n-r)!), we can calculate each combination separately and then multiply them.

So, the total number of different ways Brett can plan the menu is:

18C4 * 12C4 * 14C2 = (18! / (4! * (18-4)!)) * (12! / (4! * (12-4)!)) * (14! / (2! * (14-2)!)).