Question

Lorenzo is planning a banquet for 125 guests. He needs to select 4 appetizers, 2 entrees, and 3 side dishes. Carson's Catering has 12 appetizers, 9 entrees, and 5 side dishes to choose from. How many different ways are there for Lorenzo to plan the menu

Answer 1

178,200 ways

Explanation:

Given that :

Here,

Lerenzo can choose ;

4 appetizers from 12 = 12C4

2 entrees from 9 = 9C2

3 side dishes from 5 = 5C3

Recall :

nCr = n! / (n-r)! r!

Number of ways = 12C4 * 9C2 * 5C3

12C4 = 12! / (12 - 4)!4! = 12! / 8!4! = 495

9C2 = 9! / (9 - 2)!2! = 9! / 7!2! = 36

5C3 = 5! / (5 - 3)!3! = 5! / 2!3! = 10

Number of ways = 495 * 36 * 10 = 178,200