Question

Jason wants to dine at five different restaurants during a summer getaway. If three of nine available restaurants serve seafood, find the number of ways that at least one

of the selected restaurants will serve seafood given the following conditions.
(a) The order of selection is important.
(b) The order of selection is not important.
(a) If the order is important, then the number of ways that at least one of the selected restaurants will serve seafood is

Answer 1

answer

C(9, 5) - C(6, 5) + C(3, 1) = 126 - 6 + 3 = 123

explanation

The first term, C(9, 5), represents the number of ways to select 5 restaurants out of 9, regardless of type. The second term, C(6, 5), represents the number of ways to select 5 non-seafood restaurants out of 6. To find the number of ways that at least one of the selected restaurants will serve seafood, we subtract the number of ways to select 5 non-seafood restaurants and add the number of ways to select exactly 1 seafood restaurant, represented by C(3, 1).

The result, 123, represents the number of ways that at least one of the selected restaurants will serve seafood.