Answer:
Step-by-step explanation:
When A, B,C are equally likely to be assigned to any one of the stations 1,2 or 3
we find that each one assigned to one station has probability 1/3
Also each person is independent of the other.
Probability that
a) All three family members are assigned to the same station
= P(ABC) to same station
= P(ABC) to 1+P(ABC) to 2 +P(ABC) to 3
=3*P(A)P(B)P(C) since independent
=
b) This would be equivalent to 1- all 3 to the same station
=
c) Every member to a different station
A has 3 choices while B has remaining 2 and C has 1
Hence prob =