<s>[INST] 4 girls and 8 boys are randomly divided into 3 groups of equal size 4 girls and 8 boys are randomly divided into 3 groups of equal size
What is the probability that there will be at least one girl in each group?
 [/INST] You can calculate the probability that all girls are in a only group, the probability that four girls are disposed in two groups and then you can use the inverse probability. The probability that all girls are in only group is: $$1\cdot \frac {3}{11}\cdot \frac{2}{10}\cdot {1}{9}$$ while the probability that all girls are disposed in  two groups is:$$1\cdot 1\cdot \frac{6}{10}\cdot \frac{5}{9}.$$ Then you can use the inverse probability $$1-(1\cdot \frac{3}{11}\cdot \frac{2}{10}\cdot \frac{1}{9})-(1\cdot 1\cdot \frac{6}{10}\cdot \frac{5}{9}).$$
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