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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: 54493
One red bottle and three blue bottles are to be arranged in a straight  [#permalink]

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26 Dec 2016, 11:09
1
1
00:00

Difficulty:

5% (low)

Question Stats:

82% (00:43) correct 18% (00:32) wrong based on 110 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

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Joined: 23 Oct 2014
Posts: 13
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
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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
Intern
Joined: 13 Jul 2017
Posts: 29
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
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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)
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Joined: 15 Feb 2017
Posts: 12
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!
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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
1
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!
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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
1
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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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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