1. **Problem statement:** A bag contains 5 white, 7 black, and 4 red balls, totaling $5 + 7 + 4 = 16$ balls. We draw 3 balls at random. We want to find the probability that all 3 drawn balls are white. 2. **Formula used:** The probability of an event is given by $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$ 3. **Total number of possible outcomes:** We are choosing 3 balls out of 16 without replacement, so the total number of ways is the combination $$\binom{16}{3} = \frac{16!}{3!(16-3)!} = \frac{16 \times 15 \times 14}{3 \times 2 \times 1} = 560$$ 4. **Number of favorable outcomes:** We want all 3 balls to be white. There are 5 white balls, so the number of ways to choose 3 white balls is $$\binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5 \times 4}{2 \times 1} = 10$$ 5. **Calculate the probability:** $$\text{Probability} = \frac{10}{560} = \frac{1}{56}$$ 6. **Interpretation:** The probability that all 3 balls drawn are white is $\frac{1}{56}$, which means it is quite unlikely but possible.