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

Step-by-step explanation:

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

Number of combinations of choosing r things out of n = $^nC_r=\dfrac{n!}{r!(n-r)!}$

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

Total number of ways to do this: $^{11}C_9\times ^{12}C_2\times^{8}C_3$

$=\dfrac{11!}{9!2!}\times\dfrac{12!}{2!10!}\times\dfrac{8!}{3!5!}\\\\=\dfrac{11\times10}{2}\times\dfrac{12\times11}{2}\times\dfrac{8\times7\times6}{3\times2}\\\\= 203280$

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