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# One red bottle and three blue bottles are to be arranged in a straight

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Math Expert
Joined: 02 Sep 2009
Posts: 41912

Kudos [?]: 129370 [0], given: 12197

One red bottle and three blue bottles are to be arranged in a straight [#permalink]

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26 Dec 2016, 11:09
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Difficulty:

5% (low)

Question Stats:

74% (00:32) correct 26% (00:10) wrong based on 92 sessions

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One red bottle and three blue bottles are to be arranged in a straight line from left to right on a windowsill. How many different unique arrangements are possible?

A. 12
B. 6
C. 4
D. 3
E. 1
[Reveal] Spoiler: OA

_________________

Kudos [?]: 129370 [0], given: 12197

Intern
Joined: 23 Oct 2014
Posts: 13

Kudos [?]: 3 [0], given: 31

Re: One red bottle and three blue bottles are to be arranged in a straight [#permalink]

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02 Jan 2017, 10:32
4!/3!
4
So the answer should be C

Kudos [?]: 3 [0], given: 31

Manager
Joined: 04 Jan 2016
Posts: 161

Kudos [?]: 71 [0], given: 419

Location: Afganistan
GMAT 1: 620 Q44 V32
GMAT 2: 600 Q48 V25
GMAT 3: 660 Q42 V39
GPA: 3.48
Re: One red bottle and three blue bottles are to be arranged in a straight [#permalink]

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21 May 2017, 12:38
It is 4.

It like arranging rbbb =$$\frac{4!}{3!}$$=4

Kudos [?]: 71 [0], given: 419

Intern
Joined: 13 Jul 2017
Posts: 29

Kudos [?]: 0 [0], given: 18

One red bottle and three blue bottles are to be arranged in a straight [#permalink]

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24 Aug 2017, 05:08
Since there are 4 slot and only one color is unique that is red so we can place at 4 different places
c is the option
4

Kudos [?]: 0 [0], given: 18

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 1471

Kudos [?]: 598 [0], given: 16

Location: India
WE: Sales (Retail)
Re: One red bottle and three blue bottles are to be arranged in a straight [#permalink]

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24 Aug 2017, 10:19
Let the blue bottles be denoted by B and the red bottle be denoted by R

There are 4 combinations possible
BBBR
BBRB
BRBB
RBBB
(Option C)
_________________

Stay hungry, Stay foolish

Kudos [?]: 598 [0], given: 16

Intern
Joined: 15 Feb 2017
Posts: 11

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

Re: One red bottle and three blue bottles are to be arranged in a straight [#permalink]

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24 Aug 2017, 13:01
Can someone explain this in terms of permutations?

I thought this is a permutations question where order matters. And the formula for permutations is Total!/Exclude!

Thanks!

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

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 1471

Kudos [?]: 598 [0], given: 16

Location: India
WE: Sales (Retail)
Re: One red bottle and three blue bottles are to be arranged in a straight [#permalink]

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24 Aug 2017, 19:44
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tittoo wrote:
Can someone explain this in terms of permutations?

I thought this is a permutations question where order matters. And the formula for permutations is Total!/Exclude!

Thanks!

Hi tittoo,

This is a question of arrangement, where n items need to be arranged and c items are similar

The general formula for this is $$\frac{n!}{c!}$$

Hope that helps!
_________________

Stay hungry, Stay foolish

Kudos [?]: 598 [0], given: 16

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1655

Kudos [?]: 852 [0], given: 3

Location: United States (CA)
Re: One red bottle and three blue bottles are to be arranged in a straight [#permalink]

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29 Aug 2017, 16:15
Bunuel wrote:
One red bottle and three blue bottles are to be arranged in a straight line from left to right on a windowsill. How many different unique arrangements are possible?

A. 12
B. 6
C. 4
D. 3
E. 1

This is a permutation with indistinguishable items problem.

Since there are a total of 4 bottles, in which 3 of them are indistinguishable blue bottles, we can arrange the bottles in 4!/(3!) = 4 ways.

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Scott Woodbury-Stewart
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Kudos [?]: 852 [0], given: 3

Re: One red bottle and three blue bottles are to be arranged in a straight   [#permalink] 29 Aug 2017, 16:15
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