Question

there are 2 works each of 3 volumes and two works each of 2 volumes. in how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated

Answer 1

$(2 \times 2) \times 3 = 12 \\ 10 \times 12 = 120 \\ so \: this \: is \: the \: answer$

Answer 2

Let us consider the four works as four groups. Group I and II have 3 works each and groups III and IV have 2 volumes each.

Number of ways of arranging 4 groups in a shelf is  

4

P  

4

​  

=4!=24 ways.

Volumes in each groups can themselves be arranged.

Group I and II can be arranged each in  

3

P  

3

​  

=3!=6 ways.

Group III and IV can be arranged each in  

2

P  

2

​  

=2!=2 ways.

Hence, total number of arrangemnts =24×6×6×2×2=3456 ways.