Question

In an eleven storey building $9$ people enter a lift cabin. It is known that they will leave the lift in groups of $2,3 $ and $4$ at different residential storeys. Number of ways in which they can get down is:

• A. $\frac{(12) !}{2 !(3 !)^{2} \cdot 4 !}$
• B. $\frac{10 !}{4}$
• C. $\frac{10 !}{4 !}$
• D. $\frac{(12) !}{(3 !)^{2} \cdot 4 !}$

Answer 1

Answer: (B)

$9$ people can be divided into groups of $2,3$ and $4$ in $\frac{9 !}{2 ! 3 ! 4 !}$ ways.
Now each group can be distributed in ${ }^{10} C _{3} \times 3 !$ ways $\Rightarrow \frac{9 !}{2 ! 3 ! 4 !} 10 \cdot 9 \cdot 8=\frac{10 !}{4}$
Note that in an eleven storeyed building there will be 10 floors.