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24 Jun 2023, 13:40
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
38% (02:01) correct
62%
(01:43)
wrong
based on 82
sessions
History
Date
Time
Result
Not Attempted Yet
In how many ways can 3 identical blue roses and 3 identical red roses be arranged in a circle ?
A. 2
B. 3
C. 4
D. 5
E. 8
A. 2
B. 3
C. 4
D. 5
E. 8
25 Jun 2023, 01:46
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Bunuel
We can have three cases -
Case 1: No roses of the same kind are together
As no two roses of the same kind can be placed together, the roses have to be arranged alternatively as shown in Figure 1 below.
Hence, we can arrange the roses only in one way.
Case 2: Two blue roses are together
We can select two roses and place them together. Once, done, the three red roses can be placed as shown in Figures 2(a) and 2(b).
The third blue rose can be placed either in position 2(a) or in position 2(b).
Hence, we can arrange the roses only in two ways.
Case 3: Three blue roses are together
In this arrangement, roses of the same kind are placed together as shown in Figure 3.
Hence, we can arrange the roses only in one way.
Total way of arranging the roses = 1 + 2 + 1 = 4
IMO C
P.S. - If someone knows a more direct method of solving such questions do share. I am wondering what if the number of roses was large.
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30 Jun 2024, 21:28
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Bunuel
KarishmaB MartyMurray GMATNinja Bunuel ; could you please explain the solution to this in a more generic way without having to use cases?
It will be difficult to solve this when the number of roses increases or there are 3 different color of roses.
Thank you!
