91Ó°ÊÓ

There are $3$novels, $2$mathematics books and $1$chemistry book. These books are to be arranged on a bookshelf in any order.

Number of arrangements = $\left(3+2+1\right)!=6!\text{ways}$

$$\begin{gathered} =6×5×4×3×2×1 \\ =720\text{ways} \end{gathered}$$

Therefore, the books can be arranged in$720$ways.

There are $3$novels, $2$mathematics books and $1$chemistry book. These books are to be arranged on a bookshelf such that the mathematics books must be together and the novels must be together.

Number of ways in which novels can be arranged = $3!$

Number of ways in which mathematics books can be arranged = $2!$

Number of ways in which Chemistry book can be arranged = $1!$

These three books can be arranged in = $3!$ways

So, total number of ways$=3!×2!×1!×3!$

role="math" localid="1647517675339" $$\begin{gathered} =\left(3×2×1\right)×\left(2×1\right)×\left(1\right)×\left(3×2×1\right) \\ =72\text{ways} \end{gathered}$$

Therefore, the books can be arranged in $72$ways.

There are $3$novels, role="math" localid="1647517993959" $2$mathematics books and $1$ chemistry book. These books are to be arranged on a bookshelf such that the novels must be together.

Total novels comprise as one group.

So, total number of groups = $4$

Number of ways in which four groups can be arranged = $4!$

Number of ways in which novels can be arranged = $3!$

So, total number of ways

role="math" localid="1647518425836" $$\begin{gathered} =4!×3! \\ =(4×3×2×1)×(3×2×1) \\ =144 \end{gathered}$$

Therefore, the books can be arranged in $144$ways.