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SN9633
Joined: 01 Aug 2023
Last visit: 12 Mar 2024
Posts: 42
Given Kudos: 50
Location: India
Schools: IIMA PGPX'25 (WA) ISB '25 (WL)
GPA: 3.75
06 Nov 2023, 00:25
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
65% (02:25) correct
35%
(02:34)
wrong
based on 639
sessions
History
Date
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Not Attempted Yet
A country is divided into exactly 4 regions. Miki is sketching a map of the country's regions and plans to choose a color scheme for her map in which each region will be exactly 1 of 3 different colors and no adjacent regions will be the same color. One possible color scheme is for Regions 1,3 and 4 to have the same color and Region 2 to have a different color. How many color schemes are possible for Mikis map?
A) 6
B) 8
C) 9
D) 24
E) 36
Attachment:
M1.png [ 13.5 KiB | Viewed 8652 times ]
26 Apr 2024, 05:40
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SN9633
A country is divided into exactly 4 regions. Miki is sketching a map of the country's regions and plans to choose a color scheme for her map in which each region will be exactly 1 of 3 different colors and no adjacent regions will be the same color. One possible color scheme is for Regions 1,3 and 4 to have the same color and Region 2 to have a different color. How many color schemes are possible for Mikis map?
A) 6
B) 8
C) 9
D) 24
E) 36
Attachment:
M1.png
Region 2 is adjacent to all three regions, while the remaining regions are adjacent only to Region 2 and thus depend only on Region 2's color.
Region 2 can be painted in one of three colors. Then, each of the remaining regions can be painted in any of the two remaining colors, making the number of different schemes equal to 3 * 2 * 2 * 2 = 24.
Answer: D.
General Discussion
06 Nov 2023, 01:44
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We have 3 colors and 4 regions. The condition is that no two adjacent regions can have the same color. Further, Regions 1, 3, and 4 are not adjacent to each other, but all are adjacent to Region 2.
So, we can calculate the number of possible color schemes as follows:
1. Choose a color for Region 2. There are 3 choices here
2. Choose colors for Regions 1, 3, and 4. Each region can be one of the two remaining (non-Region 1) colors with no other restriction since they are all non-adjacent regions. There are 2*2*2 choices here
Multiplying the choices for Region 2 with the combinations for Regions 1, 3, and 4, we get 3×8=24 possible color schemes.
So, there are 24 possible color schemes for Miki's map.
So, we can calculate the number of possible color schemes as follows:
1. Choose a color for Region 2. There are 3 choices here
2. Choose colors for Regions 1, 3, and 4. Each region can be one of the two remaining (non-Region 1) colors with no other restriction since they are all non-adjacent regions. There are 2*2*2 choices here
Multiplying the choices for Region 2 with the combinations for Regions 1, 3, and 4, we get 3×8=24 possible color schemes.
So, there are 24 possible color schemes for Miki's map.
