Respuesta :
Answer:
He can make 11,250 five-course meals after this
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem:
The options are:
10 light appetizers
12 salads
5 small entrees
7 dishes
5 desserts
He throws away
3 salads
2 kinds of dishes
So he will choose
One light appetizer, from a set of 10
One salad, from a set of 9
One entree, from a set of 5
One dish, from a set of 5
One dessret, from a set of 5.
So
[tex]T = P_{(10,1)} \times P_{(9,1)} \times P_{(5,1)} \times P_{(5,1)} \times P_{(5,1)} = \frac{10!}{(10-1)!} \times \frac{9!}{(9-1)!} \times \frac{5!}{(5-1)!} \times \frac{5!}{(5-1)!} \times \frac{5!}{(5-1)!} = 11250[/tex]
He can make 11,250 five-course meals after this
