Answer:
It is the number of ways you can arrange the letters AAABBBCCCF, indicating that three players are on team A, three on team B, and three on team C, with one the field judge F.
Each different arrangement represents one of the ways you can form three teams of 3 with a field judge.
That number of arrangments, and therefore the number of ways to divide the players as required, is
They can do it in 16,800 number of ways.
It is the number of ways you can arrange the letters AAABBBCCCF, representing that three players is on team A, three on team B, and three on team C, with one the field judge F.
Each different arrangement indicates one of the ways you can form three teams of 3 with a field judge.
Since there are 10 friends in all and there are A, B and C are repeated three times, the arrangement can be;
[tex]\dfrac{10!}{3!3!3!1!} \\\\= \dfrac{10 \times 8\times7\times6\times5}{1} \\\\= 16800[/tex]
Hence, This shows that they can do it in 16,800 number of ways.
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