Question

Jason wants to dine at four four different restaurants during a summer getaway. If twotwo of sevenseven available restaurants serve​ seafood, 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

Answer 1

`140`

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
`=2`

as there should be at least one seafood serving restaurants.

When there is one seafood serving restaurants

`=^2P_1*^5P_3`

`=(2!)/(1!)*(5!)/(2!)`

`=120`

When there are two seafood serving restaurants

`=^2P_2*^5P_2`

`=(2!)/(2!)*(5!)/(3!)`

`=20`

Total number of ways
`=120+20=140`

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
`140`