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Re: A country is divided into exactly 4 regions. Miki is sketching a map [#permalink]
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Sreejanair9633 wrote:
Attachment:
M1.png
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


We know that Miki has three available colors, they can color the map using the following logic

  • Paint Region 1 in 3 ways ⇢ No restriction
  • Paint Region 2 in 2 ways ⇢ Any color except the one used in Region 1
  • Paint Region 3 in 2 ways ⇢ Any color except the one used in Region 2
  • Paint Region 4 in 2 ways ⇢ Any color except the one used in Region 2

Total = 3 * 2 * 2 * 2 = 24

Option D
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Re: A country is divided into exactly 4 regions. Miki is sketching a map [#permalink]
Clearly, 2 is adjacent to all and 1,3,4 are completely independent

so pick color of 2 and then assign colors to rest
3x{2 +3*2] = 3x8=24
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Re: A country is divided into exactly 4 regions. Miki is sketching a map [#permalink]
gmatophobia why are we not rearranging it in 4!/3! ways?
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Re: A country is divided into exactly 4 regions. Miki is sketching a map [#permalink]
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