Question

A catering service offers 10 appetizers, 11 main courses, and 3 desserts. A customer is to select 6 appetizers, 8 main courses, 2 and desserts for a banquet. In how many ways can this be done

Answer 1

13,860 possible combinations

Step-by-step explanation:

If you have 10 appetizers, 11 main courses and 3 desserts from which to choose from, and you can only select 6 appetizers, 8 main courses and 2 desserts, you can choose this may combinations:

= [8! / 6!(8 - 6)!] x [11! / 8!(11 - 8)!] x [3! / 2!(3 - 2)!]

• 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 39,916,800
• 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
• 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
• 3! = 3 x 2 x 1 = 6
• 2! = 2 x 1 = 2

= [40,320 / 720(2)] x [39,916,800 / 40,320(6) x [6 / 2(1)]

= (40,320 / 1,440) x (39,916,800 / 241,920) x 3

= 28 x 165 x 3 = 13,860