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Five people, Ada, Ben, Cathy, Dan, and Eliza, are

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Five people, Ada, Ben, Cathy, Dan, and Eliza, are

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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.

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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.

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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

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GMAT/MBA Expert

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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
For the 3 girls to be separated, they must occupy the first, third and fifth positions, as follows:
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.

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