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Five A-list actresses are vying for the three leading roles [#permalink]

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29 Nov 2011, 01:51

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Five A-list actresses are vying for the three leading roles in the new film, "Catfight in Denmark." The actresses are Julia Robards, Merly Strep, Sally Fieldstone, Lauren Bake-all, and Hallie Strawberry. Assuming that no actresses has any advantage in getting any role, what is the probability that Julia and Hallie will star in the film together?

This is how I am doing it and I end up getting 2/5 which is not right.

I am doing the following:

Julia first (1/5) and Hallie second (1/4) = (1/5 * 1/4) OR Hallie first (1/5) and Julia second (1/4) = (1/5 * 1/4) OR Julia first (1/5) and Hallie third (1/3)=(1/5 * 1/3) OR Hallie first (1/5) and Juila third (1/3)= (1/5 * 1/3) OR Julia second (1/4) and Hallie third (1/3) = (1/4 * 1/3) OR Hallie second (1/4) and Julia third (1/3) = (1/4 * 1/3)

Five A-list actresses are vying for the three leading roles in the new film, "Catfight in Denmark." The actresses are Julia Robards, Meryl Strep, Sally Fieldstone, lauren Bake-all, and Hallie Strawberry. Assuming that no actress has any advantage in getting any role, what is the probability that Julia and Hallie will star in the film together?

Why isn't this approach right?

This is how I am doing it and I end up getting 2/5 which is not right.

I am doing the following:

Julia first (1/5) and Hallie second (1/4) = (1/5 * 1/4) OR Hallie first (1/5) and Julia second (1/4) = (1/5 * 1/4) OR Julia first (1/5) and Hallie third (1/3)=(1/5 * 1/3) OR Hallie first (1/5) and Juila third (1/3)= (1/5 * 1/3) OR Julia second (1/4) and Hallie third (1/3) = (1/4 * 1/3) OR Hallie second (1/4) and Julia third (1/3) = (1/4 * 1/3)

I add them all up which totals to 2/5

Anything wrong here?

Here is your problem: Julia first (1/5) and Hallie second (1/4) and anyone else third = (1/5 * 1/4 * 1) OR Hallie first (1/5) and Julia second (1/4) and anyone else third = (1/5 * 1/4 * 1) OR Julia first (1/5), someone other than Hallie second and Hallie third (1/3)=(1/5 * 3/4 * 1/3) OR Hallie first (1/5), someone other than Julia second, and Juila third (1/3)= (1/5 * 3/4 * 1/3) OR Someone other than Hallie and Julia first, Julia second (1/4) and Hallie third (1/3) = (3/5 * 1/4 * 1/3) OR Someone other than Hallie and Julia first, Hallie second (1/4) and Julia third (1/3) = (3/5 * 1/4 * 1/3)

When you add them up, you get 6/20 = 3/10

Another way to do it: Pick Hallie and Julia. Now you can pick the third actress in 3 ways so total number of ways of picking 3 actresses (including Hallie and Julia) = 3 Total number of ways of picking any 3 actresses out of 5 = 5*4*3/3! = 10 Probability that both Hallie and Julia will be picked = 3/10

Re: Five A-list actresses are vying for the three leading roles [#permalink]

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12 Dec 2011, 12:33

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combinatorics tell us there are ten possibilities of combinations of actresses.

n!/k!(n-k)!

5 possibilities of choices - n = 5 3 will be seleced - k = 3

5*4*3*2*1/(3*2*1)(2*1) which reduces to (5*4)/(2*1) = 10.

There are 10 possible combinations you can choose to fill the 3 spots.

Now that you know there are 10, you need to find out which how many combinations you can make with the 2 selected actresses.

Julia and Halle can be grouped with any of the other 3 actresses, but there are no other possible combinations. So there are 3 groups that Julia and Halle could both be in.

3/10 is the answer.

Nice work by the creator of this question with the actress names. They all sound gorgeous.

Re: Five A-list actresses are vying for the three leading roles [#permalink]

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18 Oct 2012, 05:45

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I have got the following solution which seems different from the ones above but results in the same answer: 3 roles for 5 actresses 3/5 chances of the first actress to get a role 2/4 chances of the second one to get a role 3/5*2/4 = 6/20 = 3/10 chances of both actresses

Re: Five A-list actresses are vying for the three leading roles [#permalink]

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20 Oct 2012, 22:16

Lstadt wrote:

Five A-list actresses are vying for the three leading roles in the new film, "Catfight in Denmark." The actresses are Julia Robards, Merly Strep, Sally Fieldstone, Lauren Bake-all, and Hallie Strawberry. Assuming that no actresses has any advantage in getting any role, what is the probability that Julia and Hallie will star in the film together?

This is how I am doing it and I end up getting 2/5 which is not right.

I am doing the following:

Julia first (1/5) and Hallie second (1/4) = (1/5 * 1/4) OR Hallie first (1/5) and Julia second (1/4) = (1/5 * 1/4) OR Julia first (1/5) and Hallie third (1/3)=(1/5 * 1/3) OR Hallie first (1/5) and Juila third (1/3)= (1/5 * 1/3) OR Julia second (1/4) and Hallie third (1/3) = (1/4 * 1/3) OR Hallie second (1/4) and Julia third (1/3) = (1/4 * 1/3)

I add them all up which totals to 2/5

Anything wrong here?

Very simple solution, i would say is Total number of ways in which you can select 3 out of 5 actresses is 5C3 = 10 Total number of ways in which you can select 2 actress for 3 slots is 3C2 = 3 (as all the actresses have same probability of getting selected)

Probability = 3/10.
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Can someone please help me understand why didnt we use permutation here. Because 1. Julia, Hallie and Meryl and 2. Hallie, Julia and Meryl

should be considered two different ways to select actresses, shouldnt it?

There are 3 different roles so selecting Julia, Hallie and Meryl is different from Hallie, Julia and Meryl. But we ignore the arrangements because we are looking for a probability.

P(Picking Hallie and Julia) = (No of ways in each Hallie and Julia will be picked)/(No of ways of picking any 3 actresses) = (3*3!)/(10*3!) Since we are calculating the probability, the arrangements of the numerator (3!) will get cancelled by the arrangements of the denominator (3!). So we can ignore them.
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Can someone please help me understand why didnt we use permutation here. Because 1. Julia, Hallie and Meryl and 2. Hallie, Julia and Meryl

should be considered two different ways to select actresses, shouldnt it?

There are 3 different roles so selecting Julia, Hallie and Meryl is different from Hallie, Julia and Meryl. But we ignore the arrangements because we are looking for a probability.

P(Picking Hallie and Julia) = (No of ways in each Hallie and Julia will be picked)/(No of ways of picking any 3 actresses) = (3*3!)/(10*3!) Since we are calculating the probability, the arrangements of the numerator (3!) will get cancelled by the arrangements of the denominator (3!). So we can ignore them.

Quote:

I still don't understand why the Probability of Picking Hallie and Julia is 3*3! and why no of ways of picking any 3 actresses is 10*3!. Could you explain this to me?

Probability = Favorable cases/All cases

Favourable cases are those in which Hallie and Julia are picked. In how many different ways can you pick 3 actresses such that they include Hallie and Julia? You pick Hallie, Julia and then any one of the remaining 3 actresses. So the third actress can be picked up in 3 ways. There are 3 different roles and 3 actresses now. So they can be arranged in 3 roles in 3! ways. So our favourable cases are 3*3!

How many total cases are there? From the 5 actresses, we have to choose any 3. We can do this in 5C3 ways. 5C3 = 5*4*3/3*2*1 = 10 (Using the combination formula) Now we arrange the 3 actresses in 3 different roles in 3! ways. So total ways = 10*3!

Re: Five A-list actresses are vying for the three leading roles [#permalink]

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30 May 2015, 07:09

Please help with this question

I calculated this as 1/5 * 1/5* 3/5 ... but this is wrong in official solution they said when first actress is selected it impacts probability for second actreess to get selected. But in question stem they have not said "one by one selected" ... So i am assuming all three are selected in one stroke . Please help with this understanding.
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You can also reverse the question. If we'll hire 3 actresses, we'll fire 2 of them. We can focus on the two people we're firing. We just need to be sure we don't fire Julia or Hallie. There's a 3/5 chance the first person we fire is not J or H, and then a 2/4 chance the second person we fire is not J or H. So the answer is (3/5)(2/4) = 3/10.
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Re: Five A-list actresses are vying for the three leading roles [#permalink]

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04 Sep 2015, 08:40

Hi all,

When I read the Guide 5 – Number Properties – Fifth edition of Manhattan GMAT, chapter 7 “Extra Combinatorics & Probability”, I found the problem below (in which I have many confusions):

Five A-list actresses are vying for the three leading roles in the new film, “Catfight in Denmark”. The actresses are Julia Robards, Meryl Strep, Sally Fieldstone, Lauren Bake-all, and Hallie Strawberry. Assuming that no actress has any advantage in getting any role, what is the probability that Julia and Hallie will star in the film together?

In the problem above: the answer from Manhattan is 3/10. Their explanation is below:

The number of different combinations in which the actresses can be cast in the roles, assuming we are not concerned with which actress is given which role, is 5!/(3!2!) = 5 x2 = 10. There are 3 possible combinations that feature both Julia and Hallie: (1) Julia, Hallie, Sally (2) Julia, Hallie, Meryl (3) Julia, Hallie, Lauren Therefore, the probability that Julia and Hallie will star together is 3/10.

My other solving method is below: If we don’t consider which role for which actress, the probability (prob) for Julia is 3/5 and then for Hallie is 2/4 (Domino-effect). Thus the resulting prob = 3/5 x 2/4 = 3/10 But I am still not convinced at this stage, it should be some kinds of symmetrical situation: that either Julia or Hallie may be chosen first for the role (any of the 3 roles), so the prob should be 3/10 x 2 = 3/5

So anyone could advise me whether my thinking is correct and the answer of Manhattan for this problem is insufficient?

Re: Probability - one problem from Manhattan word translations problem set [#permalink]

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01 Jan 2017, 02:03

FortMI wrote:

Hi There,

I am trying to solve below problem and am getting it wrong. However, i dont know what's the problem of my approach. Hope get your help.

Five actresses are vying for the three leading roles in the new film. The actresses are JR, MS, SF, LB, and HS. Assuming that no actress has any advantave in getting any rold, what is the probability that JR and HS wil star in the fim together?

My approach is like below.

First Actress Second Actress Third Actress Probability JH 1/5 HS 1/4 1/20 HS 1/5 JH 1/4 1/20 JH 1/5 HS 1/3 1/15 HS 1/5 JH 1/3 1/15 JH 1/4 HS 1/3 1/12 HS 1/4 JH 1/3 1/12

Probability = 2*1/20+2*1/15+2*1/12=4/10

The correct answer is 3/10

Hi

This problem is based on combinatorics. We need to choose different actresses to fill 3 possible roles.

“JR and HS will star in the film together” two role positions are already occupied and we need to choose only one actress from remaining 3 to fill one last vacancy.

3C1

Total number of possibilities to choose 3 actresses from 5 – 5C3

Re: Five A-list actresses are vying for the three leading roles [#permalink]

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08 Jul 2017, 23:39

This is how i solved this problem. Can someone please let me know if i am correct?? So there are a total of 5 stars out of which we have to select any 3.Therefore that can be done in 10 ways. Then since Hallie and Julia must be in the cast the rest one remaining position can be filled by any of the remaining 3 actress. This can be done in 3 ways (1*1*3). Therefore the total probability is 3/10

This is how i solved this problem. Can someone please let me know if i am correct?? So there are a total of 5 stars out of which we have to select any 3.Therefore that can be done in 10 ways. Then since Hallie and Julia must be in the cast the rest one remaining position can be filled by any of the remaining 3 actress. This can be done in 3 ways (1*1*3). Therefore the total probability is 3/10

Yes, your solution is perfect - it's the solution Karishma posted at the end of the second post in this thread.
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Re: Five A-list actresses are vying for the three leading roles [#permalink]

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08 Oct 2017, 02:00

Hi all,

I tried to solve the question this way: The probability of choosing Julia or Hallie as the first actress is 2/5. The probability of choosing Julia or Hallie as the second actress is 1/4. So the probability of having them both is 2/5 x 1/4 = 1/10.

Can anyone explain why my answer is wrong? Thanks!