Question

Three couples are standing find probability that a wife is with husband

Answer 1

P(E) = 1/3 is the probability.

Answer 2

Another way to figure this out would be to choose 4 different married couples to provide a chosen person (there are (84)=70
(
8 4
)
=
70
ways to do this). Then pick one member of each of the 4 chosen couples (there are 24=16
2
4
=
16
ways to do this). So altogther there are 70⋅16=1120
70
⋅
16
=
1120
ways to choose 4 people so that no two are married to each other.

So the probability of none married to each other among the 4 chosen is 1120(164)=11201820=813
1120
(
16 4
)
=
1120
1820
=
8
13
.

So same as John's answer, just a different approach to counting in the problem.