none of them are married

[sanju09]

Given that there are 6 married couples. If we select only 4 people out of the 12, what is the probability that none of them are married to each other?

Produce your own response, links

[DanaJ]

I'd say 1*10/11*8/10*6/9 = 16/33, but probabilities is not really my strong point.....

[sureshbala]

Yes, my answer is 16/33.

[DeepakR]

Can someone please explain this ?

Thanks,
Deepak

[Brent@GMATPrepNow]

Given that there are 6 married couples. If we select only 4 people out of the 12, what is the probability that none of them are married to each other?

Produce your own response, links

One way is to treat this as a counting problem.
P(no couples) = (# ways to select 4 people with no couples)/(total number of ways to select 4 people)

Denominator: 12 people, choose 4. Can be accomplished in 12C4 ways

Numerator. First, select 4 couples from the 6 couples. This can be accomplished 6C4 ways. From each of the 4 selected couples, choose 1 member. There are
- 2 ways to select a member from the first couple
- 2 ways to select a member from the second couple
- 2 ways to select a member from the third couple
- 2 ways to select a member from the fourth couple

Total number of ways to select 4 people with no couples is 6C4x2x2x2x2

Probability = 6C4x2x2x2x2/12C4 = 16/33

[x2suresh]

Given that there are 6 married couples. If we select only 4 people out of the 12, what is the probability that none of them are married to each other?

Produce your own response, links

(12C1*10C1*8C1*6C1/4!)/12C4 = 12*10*8*6/12*11*10*9 = 48/99 = 16/33

[welcome]

12/12*10/11*8/10*6/9 = 16/33.