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A family of 2 parents and 3 children is waiting in line to order

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A family of 2 parents and 3 children is waiting in line to order  [#permalink]

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New post 29 Nov 2018, 11:45
6
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

34% (00:49) correct 66% (01:14) wrong based on 67 sessions

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A family of 2 parents and 3 children is waiting in line to order at a fast-food restaurant. Tim, the youngest child, has a tendency to cause mischief when he is not watched carefully. Because of this, the father wants to keep Tim 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 Tim?

A. 10
B. 24
C. 48
D. 60
E. 120
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Re: A family of 2 parents and 3 children is waiting in line to order  [#permalink]

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New post 29 Nov 2018, 11:54
1
Mahmoudfawzy83 wrote:
A family of 2 parents and 3 children is waiting in line to order at a fast-food restaurant. Tim, the youngest child, has a tendency to cause mischief when he is not watched carefully. Because of this, the father wants to keep Tim 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 Tim?

A. 10
B. 24
C. 48
D. 60
E. 120


The total number of arrangements of 5 people is 5!. In half of the cases father will be behind Tim and in half of the cases Tim will be behind father (as probability doesn't favor any of them). So, the needed arrangement is 5!/2 = 60.

Answer: D.
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Re: A family of 2 parents and 3 children is waiting in line to order  [#permalink]

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New post 29 Nov 2018, 11:56
Bunuel wrote:
Mahmoudfawzy83 wrote:
A family of 2 parents and 3 children is waiting in line to order at a fast-food restaurant. Tim, the youngest child, has a tendency to cause mischief when he is not watched carefully. Because of this, the father wants to keep Tim 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 Tim?

A. 10
B. 24
C. 48
D. 60
E. 120


The total number of arrangements of 5 people is 5!. In half of the cases father will be behind Tim and in half of the cases Tim will be behind father (as probability doesn't favor any of them). So, the needed arrangement is 5!/2 = 60.

Answer: D.


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Collection of Questions:
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Re: A family of 2 parents and 3 children is waiting in line to order  [#permalink]

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New post 30 Nov 2018, 02:45
2
The simplest way to solve this problem is, Total no of cases of arranging 5 people is 5! ways. Out of these, for half of the cases the father will be back of Tim and for half of the cases he will be ahead of Tim. So we need \(\frac{5!}{2}\) = 60 ways.

Or else,

Total no of ways in which Tim will be ahead of his father is:

_F_ _ _ , _ _ F _ _ , _ _ _ F _ , _ _ _ _ F

Tim can take a place ahead of his father in 1+2+3+4 = 10 ways. And remaining 3 people can be arranged is 3! ways = 6 ways. So a total of 10*6 = 60 ways.

The catch here is the question said Tim should be ahead of his father but not "just ahead" of his father. This makes the answer go from 24(if Tim stands just ahead of his father then only 24 ways are possible) to 60.

OPTION : D
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A family of 2 parents and 3 children is waiting in line to order  [#permalink]

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New post 30 Nov 2018, 04:13
1
OA:D
Number of arrangements
case 1: _ F _ _ _
1*3*2*1=6

case 2: _ _ F _ _
2*3*2*1=12

case 3: _ _ _ F _
3*3*2*1=18

case 4: _ _ _ _ F
4*3*2*1=24

Total number of arrangement =6+12+18+24=60
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Re: A family of 2 parents and 3 children is waiting in line to order  [#permalink]

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New post 30 Nov 2018, 09:11
Hi!

There is no source tag for this question.

What is the source of this question?
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Re: A family of 2 parents and 3 children is waiting in line to order  [#permalink]

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New post 30 Nov 2018, 11:12
Mahmoudfawzy83 wrote:
A family of 2 parents and 3 children is waiting in line to order at a fast-food restaurant. Tim, the youngest child, has a tendency to cause mischief when he is not watched carefully. Because of this, the father wants to keep Tim 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 Tim?

A. 10
B. 24
C. 48
D. 60
E. 120



total family size is 5

so we can consider tim and his father as 1

no of ways all of them together : 3*2*1*5 = 60 ways.. IMO D
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Re: A family of 2 parents and 3 children is waiting in line to order &nbs [#permalink] 30 Nov 2018, 11:12
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