Three persons enter a lift at the ground floor. The lift goes up to the 10th floor. The number of ways in which the three persons can exit the lift at three different floors, if the lift does not stop at the first, second, and third floors, is equal to \_\_\_\_\_\_.
Answer: 210
Solutions · 1
Official solution
The lift stops at floors 4,5,6,7,8,9,10 --- that is 7 floors.
Choose 3 of these 7 floors for the three persons to exit at: (37)=35.
Since the three persons are distinct, assign them to the 3 chosen floors in 3!=6 ways.
\[\text{Total} = 35 \times 6 = 210\]