Probability properties There are 8 letters written, but the addresses on the envelopes are written at random.
What is the likelihood that:
a) at least one of the three recipients will receive the letter intended for him?
b) Will three addressees receive the corresponding letters?
I began to reason like this:
We fix one letter that gets to its address, and the remaining 7 will not get, then the probability that one letter gets is equal to $ 1/8$.After that, it is necessary to calculate the probability of the remaining seven letters that will not get to their addressees. Unfortunately at this point I am stuck. I think to use the formula:
$$
|A|=C_{2}^2=2
$$
$$
|\Omega| = C_{7}^2\cdot\ C_{6}^1=126.
$$
$$
\mathbb P(A)= \frac{|A|}{|\Omega|}\ = \frac{2}{126}=0.01587
$$
But I'm not really sure. Can you help with this part?

Hints

*

*Have a look at derangements.

*a) $P(\text{at least one receives})=1-P(\text{nobody receives})$

*b) Find the probability that Albert, Bernard and Cynthia receive and the others do not. Of course there are more possibilities (how many?) and this with equal probability.

