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

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

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

by BTGmoderatorLU » Fri Nov 23, 2018 2:57 pm

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Source: Economist GMAT

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

The OA is C

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Source: Beat The GMAT — Problem Solving | Fri Nov 23, 2018 2:57 pm

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Fri Nov 23, 2018 5:35 pm

BTGmoderatorLU wrote:Source: Economist GMAT

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

\[4\,\,{\text{blocks}}\,\,\left\{ \begin{gathered}
\,1\,\,{\text{double}}\,\,\left( {{\text{father - mother}}} \right)\,\,\,\,\,\left[ * \right] \hfill \\
\,3\,\,{\text{singles}}\,\,\left( {{\text{each}}\,\,{\text{child}},\,\,{\text{dog}}} \right) \hfill \\
\end{gathered} \right.\]
\[?\,\,:\,\,\# \,\,{\text{4 - blocks}}\,\,{\text{arrangements}}\,\,\left( {{\text{permutations}}} \right)\]
\[? = 4! \cdot \underbrace {2!}_{\left( * \right)} = 48\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Fri Nov 23, 2018 11:22 pm

BTGmoderatorLU wrote:Source: Economist GMAT

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

The OA is C

Since the father insists of standing by his woman, let's consider them as one unit. So, there are 4 members now (Father-Mother), 2 children and a dog.

The number of ways, 4 members can stand in a row = 4! = 24

Note that upon considering that the father insists of standing by his woman, we did not consider two possibilities: 1. Father on the left of the mother; and 2. Father on the right of the mother

Thus, the total number of different arrangements = 2*24 = 48

The correct answer: C

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Mar 29, 2019 6:43 am

BTGmoderatorLU wrote:Source: Economist GMAT

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

The OA is C

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.

Answer: C

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