Doubt on statistics problem

[titoestrada]

Question 4, page 195, Manhattan GMAT Word Translations.

If Lauren, Mary, Nancy, Oprah, andy Penny sit randomly in a row, what is the probability that Oprah and Penny are NOT next to each other?

I solved it like this:

There are 5! ways in which the girls can sit = 120

There are 8 arrangments in wich Oprah and Penny are next to each other.

8/120 = 1/15 That is the probability in which they are sitting next to each other.
1 - 1/15 = 14/15 final answer.

What is wrong with this??? I do not understand why you have to multiply the ways in which the three other girls can be arranged.

thanks ;)

[gokul_nair1984]

I don't know how MGMAT approached this solution as I do not own their material. However, this is how I would:

If Lauren, Mary, Nancy, Oprah, andy Penny sit randomly in a row, what is the probability that Oprah and Penny are NOT next to each other?

_ _ _ _ _
5 girls can be arranged in 5! ways =120.

Let the bolded dashes be Oprah and Penny.Treat them as 1 unit and let's calculate the number of ways in which they will be together.

this can be given by: 4!(treating the two as one unit as they will always be together) * 2!(oprah and Penny could interchange their positions)=48

Therefore, probability that they will always be together can be given by 48/120 =2/5

Therefore, probability that they will never be together is 1-(2/5)=3/5

This is by far the simplest way possible-in my view. The method which you are suggesting will take much more time. You first have to figure out the 8 possibilites and then multiply it by the number rearrangement of other 3 girls' (6). This is also quite complicated.

[titoestrada]

Thank you, this method is easier than the one suggested.

[StaceyKoprince]

Please read (and follow!) the forum guidelines before posting.

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gokul, thanks for responding! This is a good lesson: there are always multiple ways of doing any problem, and the best way for you might not be the best way for someone else, so ask around when you don't like the first explanation you see or hear!