Question

There are 8 students lined up at the classroom door. What is the probability that Laura and Kimiko will end up next to each other if the students arrange themselves blindfolded?

Answer 1

Consider Laura and Kimiko as 1, then we have in total 7 students, which can be arranged in 7! ways.

For any of the 7! arrangements where Laura is to the left of Kimiko, there is another where Kimiko is to the left of Laura.

So there are 2*7! arrangements where Laura and Kimiko are next to each other.

In total there are 8! arrangements in a line (permutations) of the eight students.

So P(Laura is next to Kimiko)=$\frac{2*7!}{8!}= \frac{2*7!}{8*7!}= \frac{2}{8}= \frac{1}{4}=0.25$