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6 married couples

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by sh.nada » Sat Apr 23, 2011 3:03 pm
6 married couples are present at the party. if 4 people are selected out of these 12, what is the probability that none of these people will be married to each other ?

A) 1/33
B) 2/33
c) 1/3
D) 16/33
E) 11/12
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by Stuart@KaplanGMAT » Sat Apr 23, 2011 5:28 pm
sh.nada wrote:6 married couples are present at the party. if 4 people are selected out of these 12, what is the probability that none of these people will be married to each other ?

A) 1/33
B) 2/33
c) 1/3
D) 16/33
E) 11/12
Hi!

Whenever you make multiple simultaneous selections, you can treat the question as though you're selecting the items one at a time; let's do that on this question.

Our first person can be anyone, so there's a 12/12 chance that the person is "safe".

Once we choose our first person, there are 10 remaining people who aren't a spouse of that person. So the probability that the second person isn't a spouse is 10/11.

Now that we've chosen two non-spouses, 8 of the remaining 10 people aren't a spouse of either person that we've chosen. Accordingly, the probability that the third person isn't a spouse is 8/10.

Finally, when we choose our fourth person, 6 of the remaining 9 people aren't spouses of any of our 3 choices. So, the probability that the fourth person chosen is a non-spouse is 6/9.

We're making multiple selections, so we multiply the individual probabilities:

12/12 * 10/11 * 8/10 * 6/9

= (10*8*6)/(11*10*9)

= 8*6/11*9

= 48/99

= 16/33

choose (D)!
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by sh.nada » Sun Apr 24, 2011 4:40 am
Thank you very much..Awesome explaination
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by Brent@GMATPrepNow » Sun Apr 24, 2011 5:49 am
sh.nada wrote:6 married couples are present at the party. if 4 people are selected out of these 12, what is the probability that none of these people will be married to each other ?

A) 1/33
B) 2/33
c) 1/3
D) 16/33
E) 11/12
Although I prefer the solution that applies the rules of probability (Stuart's solution), it's important to note that many probability questions can be solved by counting.

Here, P(no couples in the selection of 4 people) = (number of ways to select 4 people with no couples)/(total number of ways to select 4 people)

There are various approaches here. I'll use the Fundamental Counting Principle.

Beginning with the denominator: total number of ways to select 4 people
Let's treat the 4 people as though order matters (we can do this for this question as long as we treat the numerator the same way.
Stage 1: Select the first person. This can be accomplished in 12 ways.
Stage 2: Select the second person. This can be accomplished in 11 ways (since we already selected 1 person in stage 1)
Stage 3: Select the third person. This can be accomplished in 10 ways.
Stage 4: Select the fourth person. This can be accomplished in 9 ways.
Total number of ways to select 4 people (if we say that order matters)= 12x11x10x9

Now find the number of ways to select 4 people with no couples
Stage 1: Select the first person. This can be accomplished in 12 ways.
Stage 2: Select the second person. Since we cannot have any couples in the 4 people, we must remove the spouse of the first selection from the options. So, there are 10 people to choose from, which means this can be accomplished in 10 ways.
Stage 3: Select the third person. Now that we have selected 2 people, we must remove the spouses of these 2 people from the list of options for selecting the 3rd person. So, this stage can be accomplished in 8 ways.
Stage 4: Select the fourth person. Similarly, this can be accomplished in 6 ways.
Total number of ways to select 4 people with no spouses (if we say that order matters) = 12x10x8x6

So, P(no couples in the selection of 4 people) = (number of ways to select 4 people with no couples)/(total number of ways to select 4 people)
= (12x10x8x6)/(12x11x10x9)
= 16/33
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by sana.noor » Tue Jul 30, 2013 10:04 am
stage #1: choosing 4 people out of 12 people as: 12C4 = 495 ways
stage # 2: choosing 4 couples out of 6 as 6C4: 15 ways
out of these 4 couples we can choose one person from each couple
choosing first person: 2 ways (either male or female)
choosing 2nd person: 2 ways
choosing 3rd person: 2 ways
and choosing 4th person: 2 ways
15. 2.2.2.2 = 240

240/495 = 16/33 D


is my approach to answer this question right?
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