In every detergent box there is one of these three letters, $(H,M,O)$. The three letters are found with the same probability. What is the probability of making the word $HOMO$ buying ten detergent boxes. Solve the problem using the inclusion-exclusion principle.
The probability that at least one of the letters is not inside the box when we buy the 10 boxes is $(1-1/3)^{10}$ for one letter(event $A_1$), for two letters is $(1-2/3)^{10}$ (event $A_2$) and for the three letters is $0$,(event $A_3$) If I had to make the word $HOM$, I would find the complementary of $P(A_1\cup A_2\cup A_3$). But with the repetition of the letter "O", I don't know how to tackle the problem.