From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective…

From a lot of $\displaystyle 12$ items containing $\displaystyle 3$ defectives, a sample of $\displaystyle 5$ items is drawn at random. Let the random variable X denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $\displaystyle X$ is $\displaystyle \frac{m}{n}$, where $\displaystyle \operatorname{gcd}(m, n)=1$, then $\displaystyle n-m$ is equal to $\displaystyle \_\_\_\_$.