Police ask 5 witnesses, one by one, to identify their suspects among 6 people lined up in front of a wall.

Question

Find probability that exactly 3 witnesses point at the same person.

Please leave answer as an expression.

 

Answer 1

(1/1)x(1/6)x(1/6)x(5/6)x(5/6)

 

First person can choose anyone (theoretically) - 1/1

Second person has to choose the same person (1/6)

Third person has to choose the same person (1/6)

Since this asks for exactly 3 witnesses, the other 2 must choose differently, which leaves them with the 5 other suspects

Fourth person 5/6

Fifth person 5/6

Order does not matter.