I have a problem:
If you have 10 balls labeled from 1 to 10, is the probability that the number of the draw matches the number of the ball $1 - d(10)/10!$ where $d(10)$ is the number of derangements of 10 balls?
I have a problem:
If you have 10 balls labeled from 1 to 10, is the probability that the number of the draw matches the number of the ball $1 - d(10)/10!$ where $d(10)$ is the number of derangements of 10 balls?
This would be the probability that at least one ball number matches the order of the draw. The number of derangements is given in A000166 It is approximately $\frac{10!}{e}$