four people are standing in a circle as shown. each person is given a t-shirt to wear. the shirts come in 3 different colors, and any two people next to each other cannot wear the same color shirt. how many ways are there to give t-shirts to the four people?

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19-12-2022
Mathematics

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four people are standing in a circle as shown. each person is given a t-shirt to wear. the shirts come in 3 different colors, and any two people next to each other cannot wear the same color shirt. how many ways are there to give t-shirts to the four people?

Answer :

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debjitbhowal4568 debjitbhowal4568 · Answer 1 · 2022-12-25T01:58:54-05:00

There are 3 x 2 x 2 x 1 = 12 possible ways to give t-shirts to the four people.

Here, there are 3 choices for the first person's shirt color, and 2 choices for the second person's shirt color (since they cannot wear the same color as the first person). This gives 3 × 2 = 6 total options for the first two people. For the third person, there are 2 choices for their shirt color (since they cannot wear the same color as either of the first two people). This gives a total of 6 × 2 = 12 options for the first three people. Finally, the fourth person has only 1 choice for their shirt color (since they cannot wear the same color as any of the previous three people). This gives a total of 12 × 1 = 12 options for all four people. Therefore, there are 12 total ways to give t-shirts to the four people.

These are the possible combinations:

Red, Blue, Green, Yellow

Red, Blue, Yellow, Green

Red, Green, Blue, Yellow

Red, Green, Yellow, Blue

Red, Yellow, Blue, Green

Red, Yellow, Green, Blue

Blue, Red, Green, Yellow

Blue, Red, Yellow, Green

Blue, Green, Red, Yellow

Blue, Green, Yellow, Red

Blue, Yellow, Red, Green

Blue, Yellow, Green, Red

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