fighter wrote:

prude_sb wrote:

Yes 8/35

We need to select one person out of each couple (2C1) of the 4 couples

Total number of ways: 2^4

Total number of ways of selecting 4 ppl out of 8 ppl is 8C4

Probability = (2*2*2*2)*(4*3*2*1)/(8*7*6*5) = 8/35

Ok you are choosing 4 people one person from each of the four couples,but this is not correct because you can choose a married couple but only that they shouldnt be the dancing pair

Example you can choose

M1W1 W3 M4

but though you have chosen M1 W1

M1 dances with W3 and M4 dances with W1 so none of them is dancing with their own spouse

Yes you are right . Let me try again

Number of ways by which we can select 2 couples from 4 couples = 4C2

So the probability that the couples never dance together is

1 - 4C2/8C4 = 1 - 2*3/(2*7*5) = 66/70