Question

An elevator starts at the basement with 8 people (not including the elevator operator) and discharges them all by the time it reaches the top oor, number 6. in how many ways could the operator have perceived the people leaving the elevator if all people look alike to him? what if the 8 people consisted of 5 men and 3 women and the operator could tell a man from a woman?

Answer 1

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 $\binom{13}{5}=1287$ 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 $\binom{10}{5}=252$ ways.

Number of ways to select women= 3+6-1=8

Applying combination $\binom{8}{5}=56$ ways

Total number of ways = 252*56 = 14112 ways.