A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the 10^ th floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to :
C. 7056
Total number of persons = 9 The lift goes up to the 10^ th floor but does not stop at the 1^ st and 2^ nd floors. Thus, the available floors for the persons to exit are from the 3^ rd to the 10^ th floor. Number of available floors = 8 The number of ways to select 4 persons out of 9 to form the first group is ^ 9 C_ 4 . The remaining 5 persons automatically form the second group. ^ 9 C_ 4 = 9 8 7 6 4 3 2 1 = 126 Now, these two distinct groups must exit at two different floors out of the 8 available floors. The number of ways to assign 2 different floors to the 2 groups is ^ 8 P_ 2 . ^ 8 P_ 2 = 8 7 = 56 Total number of ways = 126 56 = 7056 Answer: 7056
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