Mykel is planning a banquet for 150
guests. He needs to select 4
appetizers, 3
entrees, and 3
side dishes. Carson's Catering has 12
appetizers, 8
entrees, and 9
side dishes to choose from. How many different ways are there for Mykel to plan the menu?
To calculate the total number of ways Mykel can plan the menu, we need to multiply the number of options for each category.
Number of ways to choose 4 appetizers from 12: 12 choose 4 = 12! / (4!(12-4)!) = 495 ways
Number of ways to choose 3 entrees from 8: 8 choose 3 = 8! / (3!(8-3)!) = 56 ways
Number of ways to choose 3 side dishes from 9: 9 choose 3 = 9! / (3!(9-3)!) = 84 ways
Total number of ways to plan the menu = 495 * 56 * 84 = 2238720 ways
Therefore, there are 2,238,720 different ways for Mykel to plan the menu.