Final answer:
Frankie and Johnny's requirement to sit next to each other reduces the problem of seating 5 people to seating 4 entities since they are treated as one. Arrangements can then be calculated as 4 factorial for the entities multiplied by 2 factorial for Frankie and Johnny's order, resulting in 48 different ways.
Step-by-step explanation:
To determine in how many ways 5 people can sit in a row of 5 seats with Frankie and Johnny wanting to sit next to each other, we can treat Frankie and Johnny as a single entity since they must sit together. Thus, we have 4 entities to arrange: the 'Frankie and Johnny' pair and the 3 other people.
The number of ways to arrange these 4 entities is 4 factorial (4!). Since Frankie and Johnny can switch places within their pairing, we must multiply this arrangement by 2 factorial (2!) for the two arrangements they can have between themselves. Therefore, the total number of ways they can be seated is 4! × 2! which equals 24 × 2 = 48 different ways.