A building has ground floor and 10 more floors. Nine persons enter a lift at the ground floor. The lift goes up to the 10th floor. The number of ways in which any 4 persons exit at one floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and second floors, is equal to:
Solutions · 1
Official solution
Choose which 4 of the 9 persons form the group of 4 (the rest automatically form the group of 5): (49)=4!5!9!=126 ways.
The lift stops only at floors 3 to 10, i.e. 8 floors. Choose 2 distinct floors for the two groups: (28)=28, then assign which floor is for the group of 4 and which for the group of 5: 2 ways.
\[\text{Total} = 126 \times 28 \times 2 = 7056\]