There are five students $_1, _2, _3, _4$ and $_5$ in a music class and for them there are five seats $_1, _2,_3,_4$ and $_5$ arranged in a row, where initially the seat $_$ is allotted to the student $_$, =1,2,3,4,5. But, on the examination day, the five students are randomly allotted the five seats.
For =1,2,3,4, let $_$ denote the event that the students $_$ and $_{+1}$ do NOT sit adjacent to each other on the day of the examination. Then, find the probability of the event $_1\cap_2\cap_3\cap_4$.
I'll try again..........I don't see an easy method to determine the number of ways students S1 to S5 do not sit adjacent to a consecutive numbered student, other than counting.
I came up with $13524, 14253, 24153, 24135, 25314, 31425, 31524, 35142, 35241, 41352, 42531, 42513, 52413, 53142$.
This makes a total of $14$ seating arrangements out of $5!$ seating possibilities. Hence $P(_1\cap_2\cap_3\cap_4) = \frac{14}{5!} = \frac{7}{60}$
The downside of this method is that it is easy to miss a seating combination.....which I did.