Question

There are 6 couples(so total 12 people). Find the number of ways in which you can select 4 people( 2 m and 2 f) such that none of them is a couple.

Answer 1

Another way to figure this out would be to choose 4 different married couples to provide a chosen person (there are (84)=70 ways to do this). Then pick one member of each of the 4 chosen couples (there are 24=16 ways to do this). So altogther there are 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.

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

Answer 2

There are 6 couples(so total 12 people). Find the number of ways in which you can select 4 people( 2 m and 2 f) such that none of them is a couple.
Another way to figure this out would be to choose 4 different married couples to provide a chosen person (there are (84)=70 ways to do this). Then pick one member of each of the 4 chosen couples (there are 24=16 ways to do this). So altogther there are 70⋅16=1120