1.3. At the Faculty of Mechanics and Mathematics of Moscow State University, there are $n$ female students and $2 n-1$ male students (both female and male students are numbered). It is known that the $k$-th female student is acquainted with male students numbered from 1 to $2 k-1$. How many ways are there to form $n$ pairs, each consisting of an acquainted male and female student?

## Second Round
1.3. Solution. Notice that the student with number 1 can choose exactly 1 student to be her partner. After this, the second student chooses a partner from $3-1=2$ students. In general, the $k$-th student chooses a partner from $2 k-1-(k-1)$ students. Thus, the answer is equal to $n$ !.

## Second Round