De Montmort's Problem of Coincidence
If n objects labelled 1 to n are randomly placed in a row, what is the probability that exactly m of the objects will be correctly placed?
The equation is given below:
First, let's look at the case n=4 and m=4.
The equation correctly gives
Having all of the objects in their correct place is only 1 way out of 4! ways to arrange the 4 objects.
Can anyone explain to me the case when m=3 and n=4?
By right, it should return also , as if 3 out of 4 objects werein their correct place, then surely the last object must be in its place too.
But how does the formula make me see this?
Please can anyone help.