Question

Jason wants to dine at three different restaurants during a summer getaway. If two of six available restaurants serve​ seafood, find the number of ways that at least one of the selected restaurants will serve seafood given the following conditions.
The order of selection is important.

Answer 1

54 is the answer

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 3 out of 5 in a particular order = 5P3

$=5 ! /(5-3) !$ = 60

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

Number of selections in which all restaurants do not serve seafood = 3P3 = 6

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

= 60 minus 6  = 54