Question

Jason wants to dine at five different restaurants during a summer getaway. If two of nineavailable restaurants serve seafood, find the number of ways that at least one of theselected restaurants will serve seafood given the following conditions.a) The order of selection is important.b) The order of selection is not important.

Answer 1

Solution

Explanation:

If order is important, permutations can be used to find the number of ways the event can take place

Number of ways to select any 5 out of 8 in a particular order = 8P5

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

$8P_5=6720$

Number of restaurants serving seafood = 2 , Number of restaurants not serving seafood = 3

Number of selections in which all restaurants do not serve seafood = 5P3 = 20

Number of ways such that at least one of the selected restaurants will serve seafood = Total number of selections - Number of selections in which all restaurants do not serve seafood

$6720-20=6700$