Probability sitting at a round table What is the probability that 6 individuals will be seated correctly in order of their height when at a round table?

Is it 1/6!?

1 Because it can only be ascending or descending, and 6! on the bottom for all 6 possibilities?
We fix the first person and arrange all others. we have $5!$ possibilites for this arrangement- only two of these yield the wanted arrangement, thus the solution is $\frac{2}{5!}$
Start with the tallest person. This person can sit in one of $6$ positions. Now, the next tallest can go either left or right of that person, so that's $2$ options there. The rest is now fixed.

So, it is $6 \cdot 2= 12$ out of $6!$, i.e. $\frac{12}{6!}$