Bruised apples: binomial and sample proportion

In a random sample of four apples, find the probability that exactly three are bruised.

Let $\hat{P}$ be the random variable representing the proportion of bruised apples in random samples of 10 apples from the orchard.

Find $\Pr\left(\hat{P} \leq \frac{1}{10}\right)$.

Give your answer in the form $\frac{2^m}{3^n}$, where $m$ and $n$ are positive integers.