# probability sample of 26 will include 15 males and 11 female?

$34$ 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?

For finding males:

$$\frac{\binom{26}{15}}{\binom{109}{34}},$$

for finding females:

$$\frac{\binom{26}{11}}{\binom{109}{75}}.$$

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

• 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) – David Peterson Feb 13 '14 at 6:48

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