Guestion $03$

$\backslash$table$[[\backslash$table$[[$Elevator $1],[$Capacity$],[10$ person$],[($Max$)]],\backslash$table$[[$Elevator $2],[$Capacity$]],\backslash$table$[[$Elevator $3],[($Max$)]]]]$

In the year $2050,$

$9$ men, $8$ women and $8$ robots are waiting in front of these elevators. All of them plan to enter into the initially empty elevators altogether. What is the probability that all the men get into elevator $1$ and no robot share the same elevator with men?

$[$Hint: i$.$ Calculate the total number of ways they can use the elevators following the capacity. That is your $||.$

ii$.$ Calculate the number of ways to use the elevators following the conditions in the $2$nd third sentence$]$