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Two red bottles, two yellow bottles, and one blue bottle are to be arranged in a straight line from left to right on a windowsill. How many different unique arrangements are possible?
A. 30
B. 24
C. 12
D. 10
E. 4
A. 30
B. 24
C. 12
D. 10
E. 4
29 Mar 2017, 10:08
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Bunuel
Two red bottles, two yellow bottles, and one blue bottle are to be arranged in a straight line from left to right on a windowsill. How many different unique arrangements are possible?
A. 30
B. 24
C. 12
D. 10
E. 4
A. 30
B. 24
C. 12
D. 10
E. 4
This is a permutation with indistinguishable items problem.
Since there are a total of 5 bottles, 2 of them are indistinguishable red bottles, and 2 are indistinguishable yellow bottles, we can arrange the bottles in 5!/(2! x 2!) = (5 x 4 x 3 x 2)/(2 x 2) = 5 x 3 x 2 = 30 ways.
Answer: A
