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# The Coen family consists of a father, a mother, two children

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Manager
Joined: 18 Oct 2010
Posts: 71
The Coen family consists of a father, a mother, two children  [#permalink]

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30 May 2012, 22:13
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Difficulty:

25% (medium)

Question Stats:

68% (01:02) correct 32% (01:14) wrong based on 211 sessions

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The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his woman, as the song says?

A. 12
B. 24
C. 48
D. 60
E. 120

Bunuel your solution is required, thank you.
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Joined: 02 Sep 2009
Posts: 58347
Re: The Coen family consists of a father, a mother, two children  [#permalink]

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31 May 2012, 01:41
3
3
Joy111 wrote:
The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his woman, as the song says?

A. 12
B. 24
C. 48
D. 60
E. 120

Bunuel your solution is required, thank you.

We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that F and M are always together.

Consider F and M to be one unit, then we would have total of four units: {FM}, {C1}, {C2}, {D}. The number of arrangements of these four units is 4!, but F and M within their unit can be arranged in 2 ways: {FM} or {MF}, so total number of arrangements is 4!*2=48.

Hope it's clear.
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Manager
Joined: 13 May 2011
Posts: 191
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30 May 2012, 23:32
4!*2= 48
(Father*Mother)*c1*c2*Dog
Manager
Joined: 18 Oct 2010
Posts: 71

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30 May 2012, 23:35
BDSunDevil wrote:
4!*2= 48
(Father*Mother)*c1*c2*Dog

hi thanks but please can you elaborate,in a more simpler manner, couldn't get it
Manager
Joined: 18 Oct 2010
Posts: 71
Re: The Coen family consists of a father, a mother, two children  [#permalink]

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31 May 2012, 02:26
Bunuel wrote:
Joy111 wrote:
The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his woman, as the song says?

A. 12
B. 24
C. 48
D. 60
E. 120

Bunuel your solution is required, thank you.

We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that F and M are always together.

Consider F and M to be one unit, then we would have total of four units: {FM}, {C1}, {C2}, {D}. The number of arrangements of these four units is 4!, but F and M within their unit can be arranged in 2 ways: {FM} or {MF}, so total number of arrangements is 4!*2=48.

Hope it's clear.

Bunuel thank you +1 , please can you show me the link to more similar questions, so that I can clear my concept
Manager
Joined: 07 Apr 2014
Posts: 101
Re: The Coen family consists of a father, a mother, two children  [#permalink]

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06 Sep 2014, 05:54
1
Joy111 wrote:
The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his woman, as the song says?

A. 12
B. 24
C. 48
D. 60
E. 120

Bunuel your solution is required, thank you.

eeee.. got this question wrong.. just counted father & mother as an single entity but forget to count 2 possibility where they could be arranged by themselves.
Intern
Joined: 08 Dec 2015
Posts: 2
Re: The Coen family consists of a father, a mother, two children  [#permalink]

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30 Jan 2016, 03:46
Hello,
I don't understand why in this case we do not use the usual method: total arrangements - restrictions. For example, why in this case we can't solve it like this: 5! - 4!*2 ?
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Re: The Coen family consists of a father, a mother, two children  [#permalink]

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29 Mar 2019, 07:45
Joy111 wrote:
The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his woman, as the song says?

A. 12
B. 24
C. 48
D. 60
E. 120

Bunuel your solution is required, thank you.

Let’s call the father F, mother M, two children B and G, and the dog D. So we have FM as one unit. For example, a lineup could be [FM]BGD. Therefore, we can consider this as the arrangement of 4 distinct items, which can be arranged in 4! = 24 ways. However, since FM can also be MF, then we have a total of 24 x 2 = 48 arrangements.

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Re: The Coen family consists of a father, a mother, two children   [#permalink] 29 Mar 2019, 07:45
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