Question

In an eleventh storey building 9 people enter a lift cabin. It is known that they will leave the lift in group of 2, 3 and 4 at different residential storey. Find the number of ways in which they can get down.

Answer 1

Given that:

Floors $=9$

Floor where the person exist $=3$

Total ways $\Rightarrow 9C3=\frac{9\times 8\times 7}{3\times 2}$

$\Rightarrow 84$ ways

Let's say there are $3$ groups

$A=2$ persons

$B=3$ persons

$C=4$ persons

These floors can exist in $3!$ ways or $6$ ways

Total number of ways $=6\times 84=504$ ways

Ways in which group A ,B, C can be formed ;

${}^9{C}_2{\times }^7{C}_3{\times }^4{C}_4=1260$ ways

Hence,

The required number of ways $=1260\times 504\Rightarrow 635040.$