Let's assume there are 3 personal checks and individuals
First let's find the recurrence relation for the number of ways these checks can be place in the right envelope
[tex]P=\frac{1}{3}*\frac{1}{2}*\frac{1}{1}[/tex]Explanation: Person A has a 1/3 chance of getting the right envelope, person B has a better chance of 1/2 since envelope A is already taken, and finally, person C has a 1/1 chance
Thus, we can also write this as,
[tex]P=\frac{1}{3!}[/tex]Now, to find the recurrence relation for the number of ways these checks can be place in the n envelopes so that no check is in the right envelope, we just need to substrac 1 - P , which is,
[tex]1-\frac{1}{3!}[/tex]now, we can replace n = 3 and have a general formula,
[tex]1-\frac{1}{n!}[/tex]And that's our answer!
1 - 1/n!
