Answer :

**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

w_{1} has n_{1}, n_{2}, n_{3} as volumes

w_{2} has m_{1}, m_{2}, m_{3} as volumes

w_{3} has a_{1}, a_{2} as volumes

w_{4} has b_{1}, b_{2} as volumes

Now, firstly we have to arrange these 4 works like w_{2} w_{3} w_{1} w_{4} or w_{1} w_{2} w_{4} w_{3}

This can be done in 4! ways

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

w_{1} has 3 volumes which can be arranged like n_{2} n_{1} n_{3} or n_{3} n_{1} n_{2}

Volumes of w_{1} can be arranged in 3! ways

Similarly,

Volumes of w_{2} can be arranged in 3! ways

Volumes of w_{3} can be arranged in 2! ways

Volumes of w_{4} 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**

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