Question

A man can go by any of the 5 buses and will return by any of the remaining 4 buses ?

Answer 1

Assuming all of the 5 buses are available , in the start location and the end destinatioin troughout the time period of the journey.

The probability of man selecting one of the 5 buses for the trip=P(x)

selecting one of four other buses for the return trip P(y)

$P(x)=\frac{1}{5}\\ P(y)=\frac{^4C_1}{^5C_1}=\frac{4}{5}\\$

Therefore the probability that,A man can go by any of the 5 buses and will return by any of the remaining 4 buses is given by,

$P=P(x)\times P(y)=\frac{1}{5} \times \frac{4}{5}=\frac{4}{25}$