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**Soroban** Hello, violette!

Visualize the five teams . . . call them $\displaystyle A,B,C,D,E.$

. . $\displaystyle \begin{array}{|c|c|c|c|c|} \hline \\[-5mm]$$\displaystyle

A & B & C & D & E \\

**** & **** & **** & **** & **** \\ \hline \end{array}$

Friend #1 can be any of the 20 players:

. . $\displaystyle P(\text{friend \#1 is on a team}) \,=\,\frac{20}{20}\,=\,1$

Suppose friend #1 is on Team A.

Then friend #2 can be any of the 16 players on the other four teams.

. . $\displaystyle P(\text{friend \#2 is on a different team}) \,=\,\frac{16}{19}$

Suppose friend #2 is on Team B.

Then friend #3 can be any of the 12 players on the other three teams.

. . $\displaystyle P(\text{friend \#3 is on a different team}) \,=\,\frac{12}{18}\,=\,\frac{2}{3}$

$\displaystyle \displaystyle \text{Therefore: }\:P(\text{3 friends on different teams}) \:=\:1\cdot\frac{16}{19}\cdot\frac{2}{3} \:=\:\frac{32}{57}$