Question

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.

Answer 1

There are 1560 ways

Explanation:

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 $_{8} \mathrm{P}^{4}$. 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 $5 P^{4}$.

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

$8 P^{4}-5 P^{4}$ = 1680-120

$8 P^{4}-5 P^{4}$ = 1560

Therefore, there are 1560 ways