# Probability check

Seven male and ten female biology teachers applied for a position at a certain university where only six teachers can be accepted. In how many ways can they be accepted?

Note by Geneveve Tudence
1 year ago

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Since there are no limitations for the teachers based on gender, we see that there are a total of $$17$$ teachers and that $$6$$ teachers needed, meaning that there are $17 \text{ choose } 6 = \frac{17!}{6!(17-6!)} = \frac{17!}{6!11!} = \frac{17 \cdot 16 \cdot 15 \cdot 14 \cdot 13 \cdot 12}{6\cdot 5\cdot 4 \cdot 3 \cdot 2 \cdot 1}= \boxed{12376}$ ways to choose the teachers.

- 3 months, 1 week ago