Question

In a $12$-storey house $9$ people enter a lift cabin. It is. known that they will leave the lift in groups of $2,3$ and $4$ people at different storeys. In how many ways can they do so if the lift does not stop at the second storey?

Answer 1

Given a $12$-storey house in which a people enter a lift cabin$.$ They will leave in floor $:$ $2,3$ and $4.$

As the lift does not stop upto the $2^{nd}$ storey$,$

hence no$:$ of possible stops in lift$=12-2=10$

No$:$ of ways of choosing $3$ stops $=C_3^9=\frac{9\cdot 8\cdot 7}{3\cdot 2\cdot 1}=84$

For any particulars choice of steps$,$ no$:$ of ways for $9$ person to leave in $3$ groups$=3\cdot 2\cdot 1=6$

$\therefore$ Required no$:$ of ways$=84\times 6=504$ ways$.$