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There’s $13$ people. They’re wearing shirts of orange, green and red. The teams must sit together in a row of $13$ . But, the order can be switched around between teams. How many orders can we form

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Full solution

Q. There’s

13

people. They’re wearing shirts of orange, green and red. The teams must sit together in a row of

13

. But, the order can be switched around between teams. How many orders can we form

Define People in Shirts: Let's say there are $x$ people in orange shirts, $y$ people in green shirts, and $z$ people in red shirts, where $x + y + z = 13$ .
Calculate Arrangements: First, we need to find the number of ways to arrange the three teams (orange, green, red) in a row. That's $3!$ ways. $\newline$ Calculation: $3! = 3 \times 2 \times 1 = 6$
Consider Team Arrangements: Now, we need to consider the arrangements within each team. Since we don't know how many people are in each team, we can't calculate that yet.

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