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Three couples need to arranged in a row for a group photo. If the coup

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Math Expert
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Joined: 02 Sep 2009
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Three couples need to arranged in a row for a group photo. If the coup  [#permalink]

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New post 03 Jan 2017, 23:10
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

42% (00:57) correct 58% (00:52) wrong based on 156 sessions

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Joined: 23 Jul 2015
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Re: Three couples need to arranged in a row for a group photo. If the coup  [#permalink]

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New post 04 Jan 2017, 07:24
3
Six spots to fill. Restriction = No couple should be separated

First spot has 6 choices
Second spot has only 1
Third spot = 4 choices
Fourth spot = 1
Fifth spot = 2
Sixth spot = 1

Thus total arrangements = 6 * 4 * 2 = 48
Target Test Prep Representative
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Re: Three couples need to arranged in a row for a group photo. If the coup  [#permalink]

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New post 06 Jan 2017, 11:03
2
Bunuel wrote:
Three couples need to arranged in a row for a group photo. If the couples cannot be separated, how many different arrangements are possible?

A. 6
B. 12
C. 24
D. 48
E. 96


We need to determine in how many ways three couples can be arranged when each couple must stay together.

We can arrange the three couples as follows:

[A-B], [C-D], [E-F].

(Note: Since each couple must remain together, we have expressed each couple in a bracket.)

Since we have 3 brackets, we can arrange those 3 brackets in 3! or 6 ways. However, we must account for the individual arrangements of each couple, i.e., the number of arrangements within each individual bracket.

Couple AB can be arranged in 2! or 2 ways, couple CD can be arranged in 2! or 2 ways, and couple EF can be arranged in 2! or 2 ways.

Thus, the couples can be arranged in 6 x 2 x 2 x 2 = 48 ways.

Answer: D
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Re: Three couples need to arranged in a row for a group photo. If the coup  [#permalink]

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New post 03 Jan 2017, 23:46
1
I see this as arranging 3 people in a row. My answer would be 3!=3x2x1=6

I hope its correct. This is my first post :)

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Re: Three couples need to arranged in a row for a group photo. If the coup  [#permalink]

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New post 04 Jan 2017, 00:20
48
8 ways each group can be arranged internally & there are such 6 combination of couples possible.
.•. 6×8=48

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Re: Three couples need to arranged in a row for a group photo. If the coup  [#permalink]

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New post 04 Jan 2017, 08:48
D. 48

Since as group arrangements are 6 x couple arrangement within themselves 2x2x2
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Re: Three couples need to arranged in a row for a group photo. If the coup  [#permalink]

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New post 29 Aug 2018, 00:15
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Re: Three couples need to arranged in a row for a group photo. If the coup   [#permalink] 29 Aug 2018, 00:15
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