Question

5peoples take a lift at the ground floor of a building with three floors.the number of ways in which atleast one person gets out at each of the three floors 1,2,3 is

Answer 1

The wording of the problem indicates to me that people are to be treated as distinct.

There are just 4 possible patterns, viz. 5−1−1,4−2−1,3−3−1,and3−2−2

Compute (Choose people ) × (Permute patterns), for each pattern.

e.g. for the 3−3−1 pattern, (73)(43)(11)×3!2!,

or if you are comfortable with multinomials, (73,3,1)(32,1)

Compute similarly for each pattern, and add up. You should get the desired answer of 1806