Respuesta :
Answer:
720 ways.
Step-by-step explanation:
Given:
A catering service offers 10 appetizers, 4 main courses, and 6 desserts.
A costumer is to select 9 appetizers, 2 main courses, and 5 desserts for a banquet.
Question asked:
In how many ways can this be done ?
Solution:
By applying combination's formula:-
[tex]^{n} C_{r}=\frac{n!}{(n-r)!\ r!}[/tex]
A costumer can choose 9 appetizers out of 10 in =
[tex]^{10} C_{9}=\frac{10!}{(10-9)!\ 9!}=\frac{10\times9!}{1!\times9!} ,\ 9!\ canceled\ by\ 9! =10\ ways[/tex]
A costumer can choose 2 main courses out of 4 in =
[tex]^{4} C_{2}=\frac{4!}{(4-2)!\ 2!}=\frac{4\times3\times2!}{2!\times2!} =\frac{12}{1\times1} =12\ ways[/tex]
A costumer can choose 5 desserts out of 6 in =
[tex]^{6} C_{5}=\frac{6!}{(6-5)!\ 5!}=\frac{6\times5!}{1!\times5!} =\frac{6}{1} =6\ ways[/tex]
Total number of ways = [tex]10\times12\times6=720\ ways[/tex]
Therefore, A costumer can select 9 appetizers, 2 main courses, and 5 desserts for a banquet in 720 ways.
