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?

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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.

Infinity Mathematics - 3 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$