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A family of 2 parents and 2 children is waiting in line to order at a [#permalink]

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28 Aug 2013, 00:51

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A family of 2 parents and 2 children is waiting in line to order at a fast-food restaurant. Joey, the younger child, has a tendency to cause mischief when he is not watched carefully. Because of this, the father wants to keep Joey ahead of him in line at all times. How many different ways can the family arrange themselves in line such that the father is able to watch Joey?

A family of 2 parents and 2 children is waiting in line to order at a fast-food restaurant. Joey, the younger child, has a tendency to cause mischief when he is not watched carefully. Because of this, the father wants to keep Joey ahead of him in line at all times. How many different ways can the family arrange themselves in line such that the father is able to watch Joey?

A. 6 B. 12 C. 24 D. 36 E. 72

The total # of ways to arrange 4 people is 4!=24. In half of the cases the father will be behind Joey and in half of the cases Joey will be behind his father. So, the answer is 4!/2=12.

Re: A family of 2 parents and 2 children is waiting in line to order at a [#permalink]

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28 Aug 2013, 01:06

Bunuel wrote:

The total # of ways to arrange 4 people is 4!=24. In half of the cases the father will be behind Joey and in half of the cases Joey will be behind his father. So, the answer is 4!/2=12.

Answer: B.

Hope it helps.

Thank You. I interpreted the question as "father wants to keep Joey right ahead of him in line" and got the answer as 6.

The total # of ways to arrange 4 people is 4!=24. In half of the cases the father will be behind Joey and in half of the cases Joey will be behind his father. So, the answer is 4!/2=12.

Answer: B.

Hope it helps.

Thank You. I interpreted the question as "father wants to keep Joey right ahead of him in line" and got the answer as 6.

Yes, in this case the answer would be 6: {M}{C}{JF} --> 3!=6.
_________________

Re: A family of 2 parents and 2 children is waiting in line to order at a [#permalink]

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28 Aug 2013, 06:28

Bunuel wrote:

shreeny wrote:

A family of 2 parents and 2 children is waiting in line to order at a fast-food restaurant. Joey, the younger child, has a tendency to cause mischief when he is not watched carefully. Because of this, the father wants to keep Joey ahead of him in line at all times. How many different ways can the family arrange themselves in line such that the father is able to watch Joey?

A. 6 B. 12 C. 24 D. 36 E. 72

The total # of ways to arrange 4 people is 4!=24. In half of the cases the father will be behind Joey and in half of the cases Joey will be behind his father. So, the answer is 4!/2=12.

Bunuel, can you explain how do you conclude that half of the cases he will be ahead? Is it something to do with even numbers of people?

Thanks

I guess you didn't follow the links my previous post.

Consider this: no matter how this 4 will be arranged there can be only two scenarios, either father is behind Joey (when saying behind I mean not just right behind but simply behind, there may be any number of persons between them) OR Joey is behind father. How else? Now, ask yourself: why should one arrangement should give more ways than the other?

A family of 2 parents and 2 children is waiting in line to order at a [#permalink]

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01 Feb 2016, 07:02

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This post received KUDOS

shreeny wrote:

A family of 2 parents and 2 children is waiting in line to order at a fast-food restaurant. Joey, the younger child, has a tendency to cause mischief when he is not watched carefully. Because of this, the father wants to keep Joey ahead of him in line at all times. How many different ways can the family arrange themselves in line such that the father is able to watch Joey?

A. 6 B. 12 C. 24 D. 36 E. 72

Positions 1st2nd3rd4rd

The cases are

1. If Joe is in first position then his father can occupy any of the remaining 3 positions. 2. If Joe is in second position then his father can occupy any of the 3rd and 4th position in the order. 3. If Joe is in third position then his father can occupy only last position.

In each case the other child and parent can occupy any of the remaining 2 positions in 2! ways.

different ways as per the requirement = (3+2+1)2!=6*2=12

option B is the answer. _________________

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A family of 2 parents and 2 children is waiting in line to order at a fast-food restaurant. Joey, the younger child, has a tendency to cause mischief when he is not watched carefully. Because of this, the father wants to keep Joey ahead of him in line at all times. How many different ways can the family arrange themselves in line such that the father is able to watch Joey?

A. 6 B. 12 C. 24 D. 36 E. 72

We are given that 2 parents and 2 children are waiting in line, and we must determine in how many ways they can line up with Joey ahead of the father at all times. To determine the number of ways we can refer to the following equation:

Total number of ways to arrange the group = # ways with Joey ahead of father + # ways with Joey behind father.

Since the total number of ways in which Joey could be ahead of his father is equal to the total number of ways in which Joey could be behind his father, and since the total number of ways to arrange the group is 4P4 = 4! = 24, the number of ways in which Joey could be ahead of his father is 24/2 = 12 ways.

Answer: B
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

A family of 2 parents and 2 children is waiting in line to order at a fast-food restaurant. Joey, the younger child, has a tendency to cause mischief when he is not watched carefully. Because of this, the father wants to keep Joey ahead of him in line at all times. How many different ways can the family arrange themselves in line such that the father is able to watch Joey?

A. 6 B. 12 C. 24 D. 36 E. 72

Bunuel's and Jeff's approaches are great. I just wanted to point out that, when the answer choices are RELATIVELY SMALL (as they are here), you should also consider LISTING AND COUNTING as one of your approaches, especially if you don't identify any other approaches. In many cases, the simple process of listing outcomes will help us gain valuable insight into a fast way to solve the question.

So, if we let J = Joey, F = Father, and let A and B equal the two other people, we can start listing possible arrangements in a systematic way.