Permutations and combination s probability ?

Question

four married couples attend a dance . For the first dance the partners for the women are randomly assigned among the men. what is the probability that at least one woman must dance with her husband

Answer 1

P(at least one woman must dance with her husband)

= 1 - (d_4 / 4!)

= 1 - (9 / 24)

= 15 / 24

= 5 / 8

Answer 2

1/(4c1)

total no of combinations are 4c1(to assign  1 out of 4 gents to a lady )

probablity of getting husband for dance is 1/4

Answer 3

The probability is 15/24 = 5/8.

5/8 = 0.625

As the number of couples increases, the probability of at least one match approaches:

1 - 1/e ≈ 0.632

As you can see, it doesn't take too many pairs for the probability to be reasonably close to the limit.