Five people, Ada, Ben, Cathy, Dan, and Eliza, are lining up for a photo. What is the probability that none of the three girls will stand next to one another?
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
(E) 0.5
The OA is A .
I don't know what formula should I set. Can any expert give me some help? Please.
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Five people, Ada, Ben, Cathy, Dan, and Eliza, are
This topic has expert replies
-
EconomistGMATTutor
- GMAT Instructor
- Posts: 555
- Joined: Wed Oct 04, 2017 4:18 pm
- Thanked: 180 times
- Followed by:12 members
Hello Vincen.
Let's take a look at your question.
The only option that none of the three girls will stand next to one another is that they stand in the first, third and fifth places.
So, they have 3! options to stand. And the boys has 2! options. The total of possible options is 5!.
So, the answer is $$\frac{3!\cdot2!}{5!}=\frac{1}{10}=0.1.$$
The correct answer is A .
I hope this explanation may help you.
I'm available if you'd like a follow up.
Let's take a look at your question.
The only option that none of the three girls will stand next to one another is that they stand in the first, third and fifth places.
So, they have 3! options to stand. And the boys has 2! options. The total of possible options is 5!.
So, the answer is $$\frac{3!\cdot2!}{5!}=\frac{1}{10}=0.1.$$
The correct answer is A .
I hope this explanation may help you.
I'm available if you'd like a follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi Vincen,
We're given 3 girls and 2 boys and told to put them in a line. We're asked for the probability that none of the three girls will stand next to one another. This question can be approached in a number of different ways. Here's how you can use permutations and probability to get to the correct answer:
With 5 people, there are 5! = 120 possible arrangements. Lining up the 5 people, there's just one option for the 3 girls to NOT stand next to one another:
GBGBG = (3)(2)(2)(1)(1) = 12 options
Thus, the probability of the 3 girls NOT standing next to one another is 12/120 = 1/10 = 10% = .1
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
We're given 3 girls and 2 boys and told to put them in a line. We're asked for the probability that none of the three girls will stand next to one another. This question can be approached in a number of different ways. Here's how you can use permutations and probability to get to the correct answer:
With 5 people, there are 5! = 120 possible arrangements. Lining up the 5 people, there's just one option for the 3 girls to NOT stand next to one another:
GBGBG = (3)(2)(2)(1)(1) = 12 options
Thus, the probability of the 3 girls NOT standing next to one another is 12/120 = 1/10 = 10% = .1
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
For the 3 girls to be separated, they must occupy the first, third and fifth positions, as follows:Vincen wrote:Five people, Ada, Ben, Cathy, Dan, and Eliza, are lining up for a photo. What is the probability that none of the three girls will stand next to one another?
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
(E) 0.5
G_G_G.
P(girl occupies the first position) = 3/5. (Of the 5 children, 3 are girls.)
P(girl occupies the third position) = 2/4. (Of the 4 remaining children, 2 are girls, since 1 of the 3 girls occupies the first position.)
P(girl occupies the fifth position) = 1/3. (Of the 3 remaining children, only 1 is a girl, since 2 of the 3 girls occupy the first and third positions.)
To combine these probabilities, we multiply:
3/5 * 2/4 * 1/3 = 1/10.
The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
