## 4. On a Garden Bench

There were five of them: three boys and two girls. It was spring. They had nothing to do. They sat down next to each other on a garden bench to warm up in the sun, and they arranged themselves purely by chance. Is it more likely that the two girls will be separated from each other or that they will be sitting next to each other?
4. The number of ways to choose two seats out of five on a bench for two girls is

$$
C_{5}^{2}=\frac{5!}{3!2!}=10
$$

It is obvious (why?), that four of these ways allow the girls to sit next to each other.

Thus, we have 4 chances out of 10 that the girls will be next to each other, and 6 chances out of 10 that they will be separated from each other.

Remark. The symbol $C_{n}^{p}$ denotes the ratio

$$
\frac{n!}{p!(n-p)!}
$$