2. (10 points) Vasya has:
a) 2 different volumes from the collected works of A. S. Pushkin; the height of each volume is 30 cm;

b) the collected works of E. V. Tarle in 4 volumes; the height of each volume is 25 cm;

c) a book of lyrical poems, 40 cm tall, published by Vasya himself.

Vasya wants to arrange these books on a shelf so that his creation is in the center, and the books standing at the same distance from it on the left and right have the same height. In how many ways can this be done?
a) $3 \cdot 2!\cdot 4!$;

b) $2!\cdot 3!$;

c) $\frac{51}{3!\cdot 2!}$;

d) none of the given answers is correct.
Answer: a).

Solution: From the condition of symmetric arrangement, two conclusions can be drawn.

1) To the left and right of Vasya's poems, there should be one volume of Pushkin and two volumes of Tarle.
2) For the volumes of Pushkin, 3 pairs of positions are allowed: $(1,7),(2,6),(3,5)$. The remaining free positions must be occupied by Tarle's books.

The volumes of Pushkin can be arranged in the selected positions in 2! ways. After this, the Tarle books can be independently arranged in the remaining positions in 4! ways. Therefore, the final number of arrangements is $3 \cdot 2! \cdot 4!$.