Jason wants to dine at five different restaurants during a summer getaway. If four of nine 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.

The toal number of restaurants are 8, out of which 3 serve seafood, and during the summer gateway, Jason decided to dine out at 4 multifarious restaurants.

Since, the order is significant, permutations is to be used.

Four restaurants can be chosen from the 8 restaurants in [tex]_{8} \mathrm{P}^{4}[/tex]. In this case, "at least one" is complement of "fewer than one" (that is 0). Thus, four restaurants that are not serving seafood can be chosen from five restaurants in [tex]5 P^{4}[/tex].

Using complements principle to get the number of ways to get at least one of the restuarants serve seafood,

[tex]8 P^{4}-5 P^{4}[/tex] = 1680-120

[tex]8 P^{4}-5 P^{4}[/tex] = 1560

Therefore, there are 1560 ways

Jason wants to dine at five different restaurants during a summer getaway. If four of nine 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.

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Jason wants to dine at five different restaurants during a summer getaway. If four of nine 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.