This question is based on Combination.
Part A: when the elevator operator cannot distinguish people.
Now there are 8 people and 6 floors and the number of floors keeps decreasing by 1.
so 8+6-1=13
applying combination ways.
Part 2: When the elevator operator identifies between men and women.
there are 5 men and 3 women.
Number of ways to select 5 men = 5+6-1 =10
Applying combination ways.
Number of ways to select women= 3+6-1=8
Applying combination ways
Total number of ways = 252*56 = 14112 ways.