In a class there are 8 girls and 8 boys. The students are placed in 3 different groups with 3 students per group.
One of the groups shall contain only girls, another group shall contain only boys and the final group shall contain at least one boy and a girl. How many different possibilities are there?

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The first group can be made in (8,3) ways (or 8C3 combinations, since the order we select the 3 girls is not important) (1).
The second group can be formed also in (8,3) ways, since the order we select the 3 boys does not matter (2)....

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