You want a derangement of ten items.
A secretary randomly put 10 letters in 10 envelope
What is the probability that at least one letter was put in the correct envelope?
I solved it as follows
The probability of 0 letters in the correct envelope is
9/10 8/9.... = 9!/10!
what is my mistake ?
You want a derangement of ten items.
Suppose we arrange the envelops in strict alphabetical order.
Now randomly order the letters. There are ways to do that.
From that reference there are arrangements where no letter is in its correct alphabetical position. You are asked to find the probability that at least one is in the correct position.
.
No other way that I am aware of.
That is a simple application of the inclusion/exclusion rule on ten objects.
I don’t understand why you were asked to do this problem without having been given the tools necessary to solve it.
Have you done the inclusion/exclusion rule?