Question

A catering service offers 11 appetizers, 12 main courses, and 8 desserts. A customer is to select 9 appetizers, 2 main courses, and 3 desserts for a banquet. In how many ways can this be done?

Answer 1

Answer: 203,280

Explanation:

Given: A catering service offers 11 appetizers, 12 main courses, and 8 desserts.

Number of combinations of choosing r things out of n =
`^nC_r=(n!)/(r!(n-r)!)`

A customer is to select 9 appetizers, 2 main courses, and 3 desserts for a banquet.

Total number of ways to do this:
`^(11)C_9* ^(12)C_2*^(8)C_3`

`=(11!)/(9!2!)*(12!)/(2!10!)*(8!)/(3!5!)\\\\=(11*10)/(2)*(12*11)/(2)*(8*7*6)/(3*2)\\\\= 203280`

hence , this can be done in 203,280 ways.