Answer:
[tex]140[/tex]
Step-by-step explanation:
GIVEN: Jason wants to dine at four four different restaurants during a summer getaway. If two of seven available restaurants serve seafood.
TO FIND: find the number of ways that at least one of the selected restaurants will serve seafood given the condition that the order of selection is important.
SOLUTION:
total seafood serving restaurants [tex]=2[/tex]
as there should be at least one seafood serving restaurants.
When there is one seafood serving restaurants
[tex]=^2P_1\times^5P_3[/tex]
[tex]=\frac{2!}{1!}\times\frac{5!}{2!}[/tex]
[tex]=120[/tex]
When there are two seafood serving restaurants
[tex]=^2P_2\times^5P_2[/tex]
[tex]=\frac{2!}{2!}\times\frac{5!}{3!}[/tex]
[tex]=20[/tex]
Total number of ways [tex]=120+20=140[/tex]
Hence the number of ways that at least one of the selected restaurants will serve seafood given the condition that the order of selection is important is [tex]140[/tex]
