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

Question

One red bottle and five 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. 6
B. 12
C. 30
D. 60
E. 120

theLucifer · Answer

Possible positions : 
RBBBBB
BRBBBB
BBRBBB
BBBRBB
BBBBRB
BBBBBR
Total no. of arrangements =6 position as above *5(each blue can be selected 5C1way)
=30

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rakaisraka · Answer

Hi,
Shouldn't it be like
RBBBBB
6!/1!*5! = 6?

KS15 · Answer

Bunuel,

I think question should be 5 blue identical bottles-only in such cases can we get the answer as 6-otherwise if the bottles are not unique, then answer will be 6!=720

JeffTargetTestPrep · Answer

This is a permutation with indistinguishable items problem. The order of the bottles matters, so it is a permutation problem; however, the 5 blue bottles are indistinguishable, so we will use the indistinguishable permutations formula. We need to determine in how many ways we can arrange one red bottle and five blue bottles in a straight line from left to right.

Since there are 5 indistinguishable blue bottles, we can arrange the bottles in 6!/5! = (6 x 5 x 4 x 3 x 2 x 1 )/(5 x 4 x 3 x 2 x 1) = 6 ways.
 
Answer: A

KS15 · Answer

Jeff,

How did you say indistinguishable. Did you assume?

JeffTargetTestPrep · Answer

yes that is correct - I assumed all the red bottles were identical.

KS15 · Answer

Jeff,

I think we can't assume here. If all 6 bottles are not similar, then the answer will be different. The question needs to have the details.

JeffTargetTestPrep · Answer

I agree - more information should be added.

MathRevolution · Answer

Red bottles: 1 and the Blue bottles: 5

Total bottles: 6

To arrange '6' bottles we have 6! ways.

As the bottles are same hence,  \frac{6! }{ (1! * 5!)}  = 6

Answer A

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

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

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