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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: 77

Kudos [?]: 194 [0], given: 26

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

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30 May 2012, 22:13
2
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Difficulty:

25% (medium)

Question Stats:

66% (00:39) correct 34% (00:58) wrong based on 187 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.
[Reveal] Spoiler: OA

Kudos [?]: 194 [0], given: 26

Senior Manager
Joined: 13 May 2011
Posts: 294

Kudos [?]: 292 [0], given: 11

WE 1: IT 1 Yr
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30 May 2012, 23:32
4!*2= 48
(Father*Mother)*c1*c2*Dog

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Manager
Joined: 18 Oct 2010
Posts: 77

Kudos [?]: 194 [0], given: 26

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 42355

Kudos [?]: 133182 [1], given: 12439

Re: The Coen family consists of a father, a mother, two children [#permalink]

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31 May 2012, 01:41
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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.
_________________

Kudos [?]: 133182 [1], given: 12439

Manager
Joined: 18 Oct 2010
Posts: 77

Kudos [?]: 194 [0], given: 26

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

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Manager
Joined: 07 Apr 2014
Posts: 138

Kudos [?]: 31 [0], given: 81

Re: The Coen family consists of a father, a mother, two children [#permalink]

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06 Sep 2014, 05:54
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.

Kudos [?]: 31 [0], given: 81

Intern
Joined: 08 Dec 2015
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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] 30 Jan 2016, 03:46
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