1.3. In how many ways can six books be arranged in a row on a shelf: two volumes of Dostoevsky, two volumes of Gogol, and two volumes of Turgenev, if Dostoevsky cannot be placed next to Turgenev? (All volumes are different.)

## Second Round
1.3. Answer: 96.

Let's first solve the problem assuming that the volumes of one author are indistinguishable. Six variants arise: ГДДГТТ, ДГДГТТ, ддггтт, ддгтгт, ддгтТг, дгттгД; and six more that arise from them by replacing Dostoevsky with Turgenev, making a total of 12. To obtain the solution to the original problem, we need to multiply 12 by 8 (the books of each author can be ordered in two ways).

![](https://cdn.mathpix.com/cropped/2024_06_04_b9e7a1c03f5c15132d5ag-16.jpg?height=419&width=991&top_left_y=59&top_left_x=538)

Fig. 9: to the solution of problem 1.2

![](https://cdn.mathpix.com/cropped/2024_06_04_b9e7a1c03f5c15132d5ag-16.jpg?height=859&width=991&top_left_y=610&top_left_x=538)

Fig. 10: to the solution of problem 2.2

## Second Round