There is a group of 5 people among which there is one couple. In how many ways can these 5 people be seated in a row having 5 chairs if the couple is to be seated next to each other?

examrobotsa's picture
Q: 41 (CAPF/2022)
There is a group of 5 people among which there is one couple. In how many ways can these 5 people be seated in a row having 5 chairs if the couple is to be seated next to each other?

question_subject: 

Logic/Reasoning

question_exam: 

CAPF

stats: 

0,5,12,6,5,3,3

This combinatorics problem is about arranging people with some restrictions. The condition states that the couple must sit together, so we consider them as a single unit for counting purposes making it four units to arrange, i.e., the couple and the other three individuals.

The four units can be arranged in 4! = 24 ways. But within the couple, there are two possible orders in which they can sit (the first person of the couple can sit on the left or right), so we multiply 24 by 2 which gives us 48 ways.

So, option 1 with 24 ways is incorrect because it doesn`t take into account the two ways the couple can sit next to each other.

Option 3 with 60 ways and Option 4 with 120 ways exceed the available number of combinations and are therefore incorrect.

So, option 2 with 48 ways is the correct answer.