Given: There are two works each of 3 volumes and two works each of 2 volumes

To find: Number of ways in which these books can be arranged in a shelf provided volumes of the same work are not separated

Let w_1, w_2, w_3, w_4, are four works

w₁ has n₁, n₂, n₃ as volumes

w₂ has m₁, m₂, m₃ as volumes

w₃ has a₁, a₂ as volumes

w₄ has b₁, b₂ as volumes

Now, firstly we have to arrange these 4 works like w₂ w₃ w₁ w₄ or w₁ w₂ w₄ w₃

This can be done in 4! ways

Now, we have to separately arrange volumes of these 4 works

w₁ has 3 volumes which can be arranged like n₂ n₁ n₃ or n₃ n₁ n₂

Volumes of w₁ can be arranged in 3! ways

Similarly,

Volumes of w₂ can be arranged in 3! ways

Volumes of w₃ can be arranged in 2! ways

Volumes of w₄ can be arranged in 2! Ways

∴ Total number of ways = 4! × 3! × 3! × 2! × 2!

= 24 × 6 × 6 × 2 × 2

= 3456

Hence, the total number of ways in which these 10 books be placed on a shelf so that the volumes of the same work are not separated are 3456