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

Question

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

pranto · Answer

4!/3!
4
So the answer should be C

Heseraj · Answer

It is 4.

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

AqsaGhori · Answer

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

pushpitkc · Answer

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)

tittoo · Answer

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!

pushpitkc · Answer

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!

ScottTargetTestPrep · Answer

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.

Answer: C

bumpbot · Answer

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

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

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