$34$ of the $109$ nurses are male. If $26$ nurses are randomly selected from those employed by the hospital, what is the probability that the sample of $26$ will include exactly $15$ male (and $11$ female) nurses?

The way I was thinking about this was like this:

For finding males:


for finding females:


I am not 100% sure is this is the correct or not.

  • $\begingroup$ You are not choosing the 15 males from a population of 26, you are choosing 15 males from a population of 34 (and similarly for females) $\endgroup$ – David Peterson Feb 13 '14 at 6:48

It is

$$\dfrac{{34\choose 15}{75 \choose 11}}{{109\choose 26}}\approx 0.001$$


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