Question 1202450
The wording of the problem allows at least three different interpretations, leading to three different answers.<br>
By far the most likely interpretation is that there are 6 ways to get to the main floor (6 entrances) and then 3 ways to get to the balcony -- 2 staircases or an elevator. The answer in that case is 6*3 = 18.<br>
ANSWER (very likely the intended one): 18<br>
The other tutor uses a far less likely interpretation -- that after the 6 choices for the entrance to the main floor getting to the balcony requires using one of two staircases AND THEN an elevator. With that interpretation, the number of paths is 6*2*1 = 12.<br>
And yet a third, even less likely interpretation that is possible with the way the problem is worded is that, after the 6 choices of an entrance to the main floor, reaching the balcony requires using 2 staircases one after the other and then an elevator. With that unlikely interpretation, there is only 1 way to get from the main floor to the balcony, so the number of paths is only 6.<br>