Example 9. On five identical cards, letters are written: on two cards $l$, on the other three $i$. These cards are randomly laid out in a row. What is the probability that the word "lilii" will be formed?
Solution. Let's find the number of permutations of these five letters with repetitions. According to formula (1.3.7) for $n=5, n_{1}=2, n_{2}=3$, we get

$$
P_{5}(2 ; 3)=\frac{5!}{2!\cdot 3!}=\frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5}{1 \cdot 2 \cdot 1 \cdot 2 \cdot 3}=10
$$

This is the total number of equally possible outcomes of the experiment. The event $A$ - "the appearance of the word 'lilii'" - is favorable in one case. According to formula (1.2.1), we get

$$
P(A)=\frac{1}{10}=0.1 .
$$