1. **State the problem:** We want to find the probability that Bob plays football on exactly 2 out of the next 3 Saturdays. 2. **Identify the type of problem:** This is a binomial probability problem where the number of trials $n=3$, the number of successes $k=2$, and the probability of success on each trial $p=\frac{2}{5}$. 3. **Formula:** The binomial probability formula is $$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$ where $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ is the binomial coefficient. 4. **Calculate the binomial coefficient:** $$\binom{3}{2} = \frac{3!}{2!1!} = \frac{6}{2} = 3$$ 5. **Calculate the probability:** $$P(X=2) = 3 \times \left(\frac{2}{5}\right)^2 \times \left(1 - \frac{2}{5}\right)^{3-2} = 3 \times \frac{4}{25} \times \frac{3}{5}$$ 6. **Simplify:** $$3 \times \frac{4}{25} \times \frac{3}{5} = 3 \times \frac{12}{125} = \frac{36}{125}$$ 7. **Final answer:** The probability that Bob plays football on exactly 2 of the next 3 Saturdays is $$\boxed{\frac{36}{125}}$$ or approximately 0.288.