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

Question

One red bottle and four 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. 24
B. 12
C. 10
D. 6
E. 5

chetan2u · Answer

Hi

Logically 
There are 5 bottles out of which 4 are of one kind..
So the one which is different can be placed in any of the 5 positions..
Thus 5 ways...

Proper method 
5 things out of which 4 are same..
5 can be placed in 5! Ways but these include repetition s..
These are due to similar items, and these similar items can be placed within themselves in 4! Ways..
So answer =5!/4!=5

E

praneet87 · Answer

Since the 4 Blue bottles are not distinct. We don't need to worry about their arrangement. So we need to basically treat the red bottle as an empty space. 5 total bottles and how the Red bottle arranges amongst these 4 blue bottles.

5C4 = 5.

5C4 = 5.

Harshit401 · Answer

let 'r' be a red bottle, and 'b' be a blue bottle. we have

r & b b b b
r b b b b -1
b r b b b -2
b b r b b -3
b b b r b -4
b b b b r -5

5 is answer

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nks2611 · Answer

there are total 5 bottles and 4 are the same means identical so the will be 5!/4!= 5

hence E

Sahilkm · Answer

Total number of bottles is 5.

Number of ways of arranging these is 5!. Now 4 out of these are of one kind and rest 1 is of one kind so number of ways of arranging these is 5!/ (4! * 1!)
 ie 5
So OA is E

ScottTargetTestPrep · Answer

This is a permutation with indistinguishable items problem.

Since there are a total of 5 bottles, in which 4 of them are indistinguishable blue bottles, we can arrange the bottles in 5!/(4!) = (5 x 4 x 3 x 2)/(4 x 3 x 2) = 5 ways.

Alternate Solution:

Since there is only one red bottle, the position of the red bottle will actually determine the arrangement of the bottles. Since there are 5 spots where the red bottle can be positioned, there are 5 unique arrangements.
 
Answer: E

bumpbot · Answer

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

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