Question

$9$ persons enter a lift from ground floor of a building which stops in $10$ floors (excluding ground floor), if it is known that persons will leave the lift in group of $2,3,$ & $4$ in different floors. In how many ways this can happen?

Answer 1

Floors $=9$

Floors where the person exist $=3$

${}^9{C}_3=\frac{9\times 8\times 7}{3\times 2}=84$ ways

Lets say there are $3$ groups $A=2$ person, $B=3$ person, $C=4$person

floors can exists in $3!$ ways

i.e; $6$ ways

So Total no of ways $=6\times 84=504$,

Ways in which groups $ABC$ can be formed:-

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

$\therefore$ Required no of ways $=1260\times 504=635040$