Four engineers are working in a building of five foors (including ground floor). What is the probability that exactly three enginoors among them are working on the same floor?
Pick ONE option
A) 17625
B) 4/625
C) 1/125
D) 16/125
Answers
Given : Four engineers are working in a building of five floors (including ground floor)
To find : probability that exactly three engineers among them are working on the same floor
Solution:
There are five floors
Probability of an engineer working on any specific floor = 1/5
Probability on an engineer not working on that floor = 1 - 1/5 = 4/5
probability that exactly three engineers among them are working on the same floor
3 Floors working on a floor
⁴C₃*⁵C₁* (1/5)³ * (4/5)
⁴C₃ - ways of selecting 3 engineers .
⁵C₁ ways of selecting floor .
1/5 is the probability of each engineer working on that floor
4/5 is the probability of engineer not working on that floor
= 4 * 5 ( 1/5)³ * (4/5)
= 16/125
16/125 is the probability that exactly three engineers among them are working on the same floor
option D is correct
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